It's mentioned in Surat Nur - Verses 30-31. (link below)

See also verse number 59 in Surah, which gives the meaning of:

{O Prophet! Tell thy wives and thy daughters and the women of the believers to draw their cloaks close round them [when they go abroad]. That will be better, that so they may be recognized and not annoyed. Allah is ever Forgiving, Merciful.}

The above verses very clearly show that it is Allah Almighty Himself, Who commands the women to wear hijab, though that word is not used in the above verses. In fact, the term hijab means much more than the covering of the body; it refers to the code of modesty outlined in the verses quoted above.

Look at the expressions used: “Lower their gaze”, “be modest”, “not to display their adornment”, “draw the veils over their bosoms” “not to stamp their feet” etc.

Note: Like what is mentioned above, Women were already covering their heads, it was only the fact that it didn't completely cover their breasts/upper chest area, basically.

It must be clear to any thinking person what is meant by all the above expressions in the Holy Quran. Women in the Prophet’s time used to wear a kind of dress that covered the head, but not the bosom properly. So when they are asked to draw their veils over their bosoms so as not to reveal their beauty, it is clear that the dress must cover the head as well as the body. And hair is considered by people in most cultures of the world - not only in the Arab culture - as an attractive part of a woman’s beauty.

So, guys, please chill. Hijab is in the Qur'an and is mentioned in several saheeh ahadith (authentic sayings of the prophet).

http://www.Quran.com/24/30-31

OnIslam article about this: http://www.onislam.net/english/ask-about-islam/faith-and-worship/aspects-of-worship/166087-is-hijab-a-quranic-commandment.html