As known, Muslims don't celebrate Jesus' birth. There's even debate, whether Muhammad's birthday should be celebrated, but that's another topic in itself. Qur'anic verses 3:42-46 and 19:16-27 narrate Jesus' birth. These words '... Then (one) cried unto her from below her, saying: Grieve not! Thy Lord hath placed a rivulet beneath thee, And shake the trunk of the palm-tree toward thee, thou wilt cause ripe dates to fall upon thee. So eat and drink and be consoled...' may indicate, that Jesus was born in Summer. Indeed Jesus had no father, like the Biblical story. 'We made the Son of Mary and his mother a portent', says verse 23:50. The Qur'anic story about Jesus' miraculous birth is only short and largely confirms the Biblical story -- but for the season. Christianity celebrates Christmas at 24 and 25 December, or at 6 and 7 January -- in Winter. There's been much speculation, whether these dates are correct. Are they chosen only to correspond with ancient Midwinter celebrations? Astronomers and other scientists have tried to pinpoint the apparition of the symbolic Star of Bethlehem. This star is an important Christian symbol, meant to announce an important birth: The birth of the King of humanity, Jesus Christ. They didn't reach a unanimous answer, as illustrates this article in Daily Mail, or this article at Earth Sky, that the actual Birth might have taken place some six to four years earlier than current year 0 AD.
Verses 4:157-159 and 19:27-36 confirm the miracle, yet also emphatically deny Jesus divine qualities -- Jesus is a man without a father. He and his mother are important personalities in human history. They are sent to humanity as a warning for a day to come, Yawm al Qiyamah, when Jesus will testify for or against each human soul, and as witnesses of Divine kindness, providence and mercy. A Muslim is, therefore, asked to revere Jesus, but not worship him as God. And, therefore, see his birthday in a more modest perspective. Verses 29:46-47 exhort us to abstain from arguing with 'the People of the Scripture', unless they do wrong, because the Scripture was revealed to them and to us, and their God is our God.
Therefore, whoever you are: Merry Birthday of Christ. Enjoy @}}-