Mary's Genealogy in Matthew?

The early universal witness of the Church is that Mary herself was a physical descendant of David, and it is for this reason that Jesus is also David's physical offspring:

Chapter 43. He concludes that the law had an end in Christ, who was born of the Virgin

Justin: As, then, circumcision began with Abraham, and the Sabbath and sacrifices and offerings and feasts with Moses, and it has been proved they were enjoined on account of the hardness of your people's heart, so it was necessary, in accordance with the Father's will, that they should have an end in Him who was born of a virgin, of the family of Abraham and tribe of Judah, and of David; in Christ the Son of God, who was proclaimed as about to come to all the world, to be the everlasting law and the everlasting covenant, even as the forementioned prophecies show. And we, who have approached God through Him, have received not carnal, but spiritual circumcision, which Enoch and those like him observed. And we have received it through baptism, since we were sinners, by God's mercy; and all men may equally obtain it. But since the mystery of His birth now demands our attention I shall speak of it. Isaiah then asserted in regard to the generation of Christ, that it could not be declared by man, in words already quoted: 'Who shall declare His generation? For His life is taken from the earth: for the transgressions of my people was He led to death.' Isaiah 53:8 The Spirit of prophecy thus affirmed that the generation of Him who was to die, that we sinful men might be healed by His stripes, was such as could not be declared. Furthermore, that the men who believe in Him may possess the knowledge of the manner in which He came into the world, the Spirit of prophecy by the same Isaiah foretold how it would happen thus:

And the Lord spoke again to Ahaz, saying, Ask for yourself a sign from the Lord your God, in the depth, or in the height. And Ahaz said, I will not ask, neither will I tempt the Lord. And Isaiah said, Hear then, O house of David; Is it a small thing for you to contend with men, and how do you contend with the Lord? Therefore the Lord Himself will give you a sign. Behold, the virgin shall conceive, and shall bear a son, and his name shall be called Immanuel. Butter and honey shall he eat, before he knows or prefers the evil, and chooses out the good; for before the child knows good or ill, he rejects evil by choosing out the good. For before the child knows how to call father or mother, he shall receive the power of Damascus and the spoil of Samaria in presence of the king of Assyria. And the land shall be forsaken, which you shall with difficulty endure in consequence of the presence of its two kings. But God shall bring on you, and on your people, and on the house of your father, days which have not yet come upon you since the day in which Ephraim took away from Judah the king of Assyria.

Now it is evident to all, that in the race of Abraham according to the flesh no one has been born of a virgin, or is said to have been born [of a virgin], save this our Christ. But since you and your teachers venture to affirm that in the prophecy of Isaiah it is not said, 'Behold, the virgin shall conceive,' but, 'Behold, the young woman shall conceive, and bear a son;' and [since] you explain the prophecy as if [it referred] to Hezekiah, who was your king, I shall endeavour to discuss shortly this point in opposition to you, and to show that reference is made to Him who is acknowledged by us as Christ...

Chapter 45. Those who were righteous before and under the law shall be saved by Christ

Trypho: If I seem to interrupt these matters, which you say must be investigated, yet the question which I mean to put is urgent. Allow me first.

Justin: Ask whatever you please, as it occurs to you; and I shall endeavour, after questions and answers, to resume and complete the discourse.

Trypho: Tell me, then, shall those who lived according to the law given by Moses, live in the same manner with Jacob, Enoch, and Noah, in the resurrection of the dead, or not?

Justin: When I quoted, sir, the words spoken by Ezekiel, that 'even if Noah and Daniel and Jacob were to beg sons and daughters, the request would not be granted them,' but that each one, that is to say, shall be saved by his own righteousness, I said also, that those who regulated their lives by the law of Moses would in like manner be saved. For what in the law of Moses is naturally good, and pious, and righteous, and has been prescribed to be done by those who obey it; and what was appointed to be performed by reason of the hardness of the people's hearts; was similarly recorded, and done also by those who were under the law. Since those who did that which is universally, naturally, and eternally good are pleasing to God, they shall be saved through this Christ in the resurrection equally with those righteous men who were before them, namely Noah, and Enoch, and Jacob, and whoever else there be, along with those who have known this Christ, Son of God, who was before the morning star and the moon, and submitted to become incarnate, and be born of this virgin of the family of David, in order that, by this dispensation, the serpent that sinned from the beginning, and the angels like him, may be destroyed, and that death may be contemned, and for ever quit, at the second coming of the Christ Himself, those who believe in Him and live acceptably — and be no more: when some are sent to be punished unceasingly into judgment and condemnation of fire; but others shall exist in freedom from suffering, from corruption, and from grief, and in immortality. (St. Justin Martyr, Dialogue with Trypho, Chapters 31-47; emphasis mine)

Chapter 100. In what sense Christ is [called] Jacob, and Israel, and Son of Man

Justin: Then what follows—'But You, the praise of Israel, inhabit the holy place'— declared that He is to do something worthy of praise and wonderment, being about to rise again from the dead on the third day after the crucifixion; and this He has obtained from the Father. For I have showed already that Christ is called both Jacob and Israel; and I have proved that it is not in the blessing of Joseph and Judah alone that what relates to Him was proclaimed mysteriously, but also in the Gospel it is written that He said: 'All things are delivered unto me by My Father.' and, 'No man knows the Father but the Son; nor the Son but the Father, and they to whom the Son will reveal Him.' Matthew 11:27 Accordingly He revealed to us all that we have perceived by His grace out of the Scriptures, so that we know Him to be the first-begotten of God, and to be before all creatures; likewise to be the Son of the patriarchs, since He assumed flesh by the Virgin of their family, and submitted to become a man without comeliness, dishonoured, and subject to suffering. Hence, also, among His words He said, when He was discoursing about His future sufferings: 'The Son of man must suffer many things, and be rejected by the Pharisees and Scribes, and be crucified, and on the third day rise again.' Matthew 16:21 He said then that He was the Son of man, either because of His birth by the Virgin, who was, as I said, of the family of David and Jacob, and Isaac, and Abraham; or because Adam was the father both of Himself and of those who have been first enumerated from whom Mary derives her descent. For we know that the fathers of women are the fathers likewise of those children whom their daughters bear. For [Christ] called one of His disciples— previously known by the name of Simon — Peter; since he recognised Him to be Christ the Son of God, by the revelation of His Father: and since we find it recorded in the memoirs of His apostles that He is the Son of God, and since we call Him the Son, we have understood that He proceeded before all creatures from the Father by His power and will (for He is addressed in the writings of the prophets in one way or another as Wisdom, and the Day, and the East, and a Sword, and a Stone, and a Rod, and Jacob, and Israel); and that He became man by the Virgin, in order that the disobedience which proceeded from the serpent might receive its destruction in the same manner in which it derived its origin. For Eve, who was a virgin and undefiled, having conceived the word of the serpent, brought forth disobedience and death. But the Virgin Mary received faith and joy, when the angel Gabriel announced the good tidings to her that the Spirit of the Lord would come upon her, and the power of the Highest would overshadow her: wherefore also the Holy Thing begotten of her is the Son of God; and she replied, 'Be it unto me according to your word.' Luke 1:38 And by her has He been born, to whom we have proved so many Scriptures refer, and by whom God destroys both the serpent and those angels and men who are like him; but works deliverance from death to those who repent of their wickedness and believe upon Him. (Ibid., Chapters 89-108; emphasis mine)

Chapter 33. Manner of Christ's birth predicted

And hear again how Isaiah in express words foretold that He should be born of a virgin; for he spoke thus: Behold, a virgin shall conceive, and bring forth a son, and they shall say for His name, 'God with us.'  Isaiah 7:14 For things which were incredible and seemed impossible with men, these God predicted by the Spirit of prophecy as about to come to pass, in order that, when they came to pass, there might be no unbelief, but faith, because of their prediction. But lest some, not understanding the prophecy now cited, should charge us with the very things we have been laying to the charge of the poets who say that Jupiter went in to women through lust, let us try to explain the words. This, then, Behold, a virgin shall conceive, signifies that a virgin should conceive without intercourse. For if she had had intercourse with any one whatever, she was no longer a virgin; but the power of God having come upon the virgin, overshadowed her, and caused her while yet a virgin to conceive. And the angel of God who was sent to the same virgin at that time brought her good news, saying, Behold, you shall conceive of the Holy Ghost, and shall bear a Son, and He shall be called the Son of the Highest, and you shall call His name Jesus; for He shall save His people from their sins, Luke 1:32; Matthew 1:21 — as they who have recorded all that concerns our Saviour Jesus Christ have taught, whom we believed, since by Isaiah also, whom we have now adduced, the Spirit of prophecy declared that He should be born as we intimated before. It is wrong, therefore, to understand the Spirit and the power of God as anything else than the Word, who is also the first-born of God, as the foresaid prophet Moses declared; and it was this which, when it came upon the virgin and overshadowed her, caused her to conceive, not by intercourse, but by power. And the name Jesus in the Hebrew language means Σωτήρ (Saviour) in the Greek tongue. Wherefore, too, the angel said to the virgin, You shall call His name Jesus, for He shall save His people from their sins. And that the prophets are inspired by no other than the Divine Word, even you, as I fancy, will grant. (Justin Martyr, First Apology)

1. Those, therefore, who allege that He took nothing from the Virgin do greatly err, [since,] in order that they may cast away the inheritance of the flesh, they also reject the analogy [between Him and Adam]. For if the one [who sprang] from the earth had indeed formation and substance from both the hand and workmanship of God, but the other not from the hand and workmanship of God, then He who was made after the image and likeness of the former did not, in that case, preserve the analogy of man, and He must seem an inconsistent piece of work, not having wherewith He may show His wisdom. But this is to say, that He also appeared putatively as man when He was not man, and that He was made man while taking nothing from man. For if He did not receive the substance of flesh from a human being, He neither was made man nor the Son of man; and if He was not made what we were, He did no great thing in what He suffered and endured. But every one will allow that we are [composed of] a body taken from the earth, and a soul receiving spirit from God. This, therefore, the Word of God was made, recapitulating in Himself His own handiwork; and on this account does He confess Himself the Son of man, and blesses the meek, because they shall inherit the earth. Matthew 5:5 The Apostle Paul, moreover, in the Epistle to the Galatians, declares plainly, God sent His Son, made of a woman. Galatians 4:4 And again, in that to the Romans, he says, Concerning His Son, who was made of the seed of David according to the flesh, who was predestinated as the Son of God with power, according to the spirit of holiness, by the resurrection from the dead, Jesus Christ our Lord. Romans 1:3-4

2. Superfluous, too, in that case is His descent into Mary; for why did He come down into her if He were to take nothing of her? Still further, if He had taken nothing of Mary, He would never have availed Himself of those kinds of food which are derived from the earth, by which that body which has been taken from the earth is nourished; nor would He have hungered, fasting those forty days, like Moses and Elias, unless His body was craving after its own proper nourishment; nor, again, would John His disciple have said, when writing of Him, But Jesus, being wearied with the journey, was sitting [to rest]; John 4:6 nor would David have proclaimed of Him beforehand, They have added to the grief of my wounds; nor would He have wept over Lazarus, nor have sweated great drops of blood; nor have declared, My soul is exceeding sorrowful; Matthew 26:38 nor, when His side was pierced, would there have come forth blood and water. For all these are tokens of the flesh which had been derived from the earth, which He had recapitulated in Himself, bearing salvation to His own handiwork.

3. Wherefore Luke points out that the pedigree which traces the generation of our Lord back to Adam contains seventy-two generations, connecting the end with the beginning, and implying that it is He who has summed up in Himself all nations dispersed from Adam downwards, and all languages and generations of men, together with Adam himself. Hence also was Adam himself termed by Paul the figure of Him that was to come, Romans 5:14 because the Word, the Maker of all things, had formed beforehand for Himself the future dispensation of the human race, connected with the Son of God; God having predestined that the first man should be of an animal nature, with this view, that he might be saved by the spiritual One. For inasmuch as He had a pre-existence as a saving Being, it was necessary that what might be saved should also be called into existence, in order that the Being who saves should not exist in vain.

4. In accordance with this design, Mary the Virgin is found obedient, saying, Behold the handmaid of the Lord; be it unto me according to your word. Luke 1:38 But Eve was disobedient; for she did not obey when as yet she was a virgin. And even as she, having indeed a husband, Adam, but being nevertheless as yet a virgin (for in Paradise they were both naked, and were not ashamed, Genesis 2:25 inasmuch as they, having been created a short time previously, had no understanding of the procreation of children: for it was necessary that they should first come to adult age, and then multiply from that time onward), having become disobedient, was made the cause of death, both to herself and to the entire human race; so also did Mary, having a man betrothed [to her], and being nevertheless a virgin, by yielding obedience, become the cause of salvation, both to herself and the whole human race. And on this account does the law term a woman betrothed to a man, the wife of him who had betrothed her, although she was as yet a virgin; thus indicating the back-reference from Mary to Eve, because what is joined together could not otherwise be put asunder than by inversion of the process by which these bonds of union had arisen; so that the former ties be cancelled by the latter, that the latter may set the former again at liberty. And it has, in fact, happened that the first compact looses from the second tie, but that the second tie takes the position of the first which has been cancelled. For this reason did the Lord declare that the first should in truth be last, and the last first. Matthew 19:30, Matthew 20:16 And the prophet, too, indicates the same, saying, instead of fathers, children have been born unto you. For the Lord, having been born the First-begotten of the dead, Revelation 1:5 and receiving into His bosom the ancient fathers, has regenerated them into the life of God, He having been made Himself the beginning of those that live, as Adam became the beginning of those who die. 1 Corinthians 15:20-22 Wherefore also Luke, commencing the genealogy with the Lord, carried it back to Adam, indicating that it was He who regenerated them into the Gospel of life, and not they Him. And thus also it was that the knot of Eve's disobedience was loosed by the obedience of Mary. For what the virgin Eve had bound fast through unbelief, this did the virgin Mary set free through faith. (St. Irenaeus, Adversus haereses, Book III, Chapter 22 Christ assumed actual flesh, conceived and born of the Virgin; emphasis mine)

Interestingly, Clement of Alexandria seems to imply that Matthew’s genealogy is that of Mary since he writes:  

And in the Gospel according to Matthew, the genealogy which begins with Abraham is continued down to Mary the mother of the Lord. For, it is said, Matthew 1:17 from Abraham to David are fourteen generations; and from David to the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon till Christ are likewise other fourteen generations,— three mystic intervals completed in six weeks. (The Stromata, or Miscellanies, Book I; emphasis mine)

Moreover, Victorinus in 260 AD wrote a commentary on Revelation where he explicitly says that Matthew lists Mary’s genealogy:

And round about the throne were four living creatures. The four living creatures are the four Gospels.

7-10. The first living creature was like to a lion, and the second was like to a calf, and the third had a face like to a man, and the fourth was like to a flying eagle; and they had six wings, and round about and within they were full of eyes; and they had no rest, saying, Holy, holy, holy, Lord Omnipotent. And the four and twenty elders, falling down before the throne, adored God. The four and twenty elders are the twenty-four books of the prophets and of the law, which give testimonies of the judgment. Moreover, also, they are the twenty-four fathers — twelve apostles and twelve patriarchs. And in that the living creatures are different in appearance, this is the reason: the living creature like to a lion designates Mark, in whom is heard the voice of the lion roaring in the desert. And in the figure of a man, Matthew strives to declare to us the genealogy of Mary, from whom Christ took flesh. Therefore, in enumerating from Abraham to David, and thence to Joseph, he spoke of Him as if of a man: therefore his announcement sets forth the image of a man. Luke, in narrating the priesthood of Zacharias as he offers a sacrifice for the people, and the angel that appears to him with respect of the priesthood, and the victim in the same description bore the likeness of a calf. John the evangelist, like to an eagle hastening on uplifted wings to greater heights, argues about the Word of God. Mark, therefore, as an evangelist thus beginning, The beginning of the Gospel of Jesus Christ, as it is written in Isaiah the prophet; The voice of one crying in the wilderness, Isaiah 40:3 — has the effigy of a lion. And Matthew, The book of the generation of Jesus Christ, the son of David, the son of Abraham: Matthew 1:1 this is the form of a man. But Luke said, There was a priest, by name Zachariah, of the course of Abia, and his wife was of the daughters of Aaron: Luke 1:5 this is the likeness of a calf. But John, when he begins, In the beginning was the Word, and the Word was with God, and the Word was God, sets forth the likeness of a flying eagle. Moreover, not only do the evangelists express their four similitudes in their respective openings of the Gospels, but also the Word itself of God the Father Omnipotent, which is His Son our Lord Jesus Christ, bears the same likeness in the time of His advent. When He preaches to us, He is, as it were, a lion and a lion's cub. And when for man's salvation He was made man to overcome death, and to set all men free, and that He offered Himself a victim to the Father on our behalf, He was called a calf. And that He overcame death and ascended into the heavens, extending His wings and protecting His people, He was named a flying eagle. Therefore these announcements, although they are four, yet are one, because it proceeded from one mouth. Even as the river in paradise, although it is one, was divided into four heads. Moreover, that for the announcement of the New Testament those living creatures had eyes within and without, shows the spiritual providence which both looks into the secrets of the heart, and beholds the things which are coming after that are within and without. (Commentary on the Apocalypse; emphasis mine)

Further Reading

Mary’s Parents: Descendants of David

Mary’s Father: Eli or Joakim?

Christ: The Physical Seed of David