In Islam, Jesus (`Isa in Arabic) is considered one of the five greatest prophets sent by God to mankind.

Muslims’ knowledge about Jesus is based on the two main sources of Islamic knowledge: the Quran and Hadith.

In the Quran, Jesus is referred to as `Isa ibn Maryam, or Jesus, the son of Mary.

The story of Mary and Jesus is best described in the Quran in the surahs of Aal `Imran and Maryam.

Mary: A Precocious Girlhood

The story starts with Mary, who was blessed as a child with God’s protection.

Mary was born to the pious household of Aal `Imran, or the family of `Imran. Many people argued for the honor of taking care of the child, but the responsibility was given to Zachariah, an elderly and childless man, who immediately noticed that the young girl was special.

One day, Zachariah noticed that the girl had in her possession certain provisions for which he could not account. He asked her how she came by the food and she answered:

{“From Allah: for Allah Provides sustenance to whom He pleases without measure.”} (3:37)

This simple answer had a deep impact on the elderly man. Having long wished for a son, the devout Zachariah prayed to God for progeny.

As the Quran relates in the verses below, his prayers were answered almost immediately, although his wife was barren and beyond childbearing age:

{Then Zachariah prayed unto his Lord and said: My Lord! Bestow upon me of Thy bounty goodly offspring. Lo! Thou art the Hearer of Prayer.

And the angels called to him as he stood praying in the sanctuary: Allah giveth thee glad tidings of (a son whose name is) John, (who cometh) to confirm a word from Allah lordly, chaste, a prophet of the righteous.} (3:38-9)

The uniqueness of Mary, noticed by Zachariah, was spelled out to her by the angels:

{Behold! The angels said: “O Mary! Allah hath chosen thee and purified thee- chosen thee above the women of all nations. O Mary! Worship thy Lord devoutly: Prostrate thyself, and bow down (in prayer) with those who bow down.”} (3:42-3)

Here the story of Mary’s upbringing and girlhood, as related in the Quran, ends.

The Miracle of Jesus

In the surah entitled “Maryam,” we hear more of this special woman’s story, best told by the Quran itself.

{Relate in the Book (the story of) Mary, when she withdrew from her family to a place in the East.

She placed a screen (to screen herself) from them; then We sent her our angel, and he appeared before her as a man in all respects. 

She said: “I seek refuge from thee to (Allah) Most Gracious: (come not near) if thou dost fear Allah.”

He said: “Nay, I am only a messenger from thy Lord, (to announce) to thee the gift of a holy son.”

She said: “How shall I have a son, seeing that no man has touched me, and I am not unchaste?”

He said: “So (it will be): Thy Lord saith, ‘that is easy for Me: and (We wish) to appoint him as a Sign unto men and a Mercy from Us’: It is a matter (so) decreed.”

So she conceived him, and she retired with him to a remote place.} (19:16–22)

From the Quranic description of events, we can deduce that Mary spent most of her pregnancy alone. What happened to her during this period is not mentioned in the Quran. The Quran picks up the story at the moment that Mary goes into labor.

{And the pains of childbirth drove her to the trunk of a palm-tree: She cried (in her anguish): “Ah! Would that I had died before this! Would that I had been a thing forgotten and out of sight!”

But (a voice) cried to her from beneath the (palm-tree): “Grieve not! for thy Lord hath provided a rivulet beneath thee;

“And shake towards thyself the trunk of the palm-tree: It will let fall fresh ripe dates upon thee.”} (19:23-4)

God, knowing the reaction of society, further guided her how to deal with the situation:

{“So eat and drink and cool (thine) eye. And if thou dost see any man, say, ‘I have vowed a fast to (Allah) Most Gracious, and this day will I enter into not talk with any human being.’”} (19:25)

When she carried the baby Jesus to her people, they questioned her; and as a baby in her arms, Jesus gave them the answer. The Quran describes this scene in detail:

{At length she brought the (babe) to her people, carrying him (in her arms). They said: “O Mary! Truly an amazing thing hast thou brought!

“O sister of Aaron! Thy father was not a man of evil, nor thy mother a woman unchaste!”

But she pointed to the babe. They said: “How can we talk to one who is a child in the cradle?”

He said: “I am indeed a servant of Allah: He hath given me revelation and made me a prophet;

“And He hath made me blessed wheresoever I be, and hath enjoined on me Prayer and Charity as long as I live;

“(He) hath made me kind to my mother, and not overbearing or miserable;

“So peace is on me the day I was born, the day that I die, and the day that I shall be raised up to life (again)”!} (19:26-33)

And so the baby Jesus defended his mother from any accusations of adultery, and in a nutshell, explained who he was and why he was sent by God.

Here ends the story of Mary and miraculous birth of one of the greatest prophets of God, Jesus.

{Such was Jesus, son of Mary: (this is) a statement of the truth concerning which they doubt.} (19:34)

http://www.onislam.net/english/reading-islam/understanding-islam/belief/messengers/442554-the-birth-of-jesus-was-described-in-the-quran.html