According to what Muslims believe to be the final revealed Word of God (the Qur'an), the biological father of Mary was Imraan. However, due to circumstances, Mary was mostly raised by her uncle, Zakary:

Allah did choose Adam and Noah, the family of Abraham, and the family of 'Imran above all people,- Offspring, one of the other: And Allah heareth and knoweth all things. Behold! a woman of 'Imran said: "O my Lord! I do dedicate unto Thee what is in my womb for Thy special service: So accept this of me: For Thou hearest and knowest all things." When she was delivered, she said: "O my Lord! Behold! I am delivered of a female child!"- and Allah knew best what she brought forth- "And no wise is the male Like the female. I have named her Mary, and I commend her and her offspring to Thy protection from the Evil One, the Rejected."

(Quran,Yusuf Ali translation, verses 3:33-3:36)