"And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed." - Surah 24 Al-Nur:31

Sahih Bukhari (6:321) - Muhammad is asked whether it is right for a young woman to leave her house without a veil. He replies, "She should cover herself with the veil of her companion."

Sahih Bukhari (60:282) - After Muhammad issued the command (Quran 24:31) for women to cover themselves, the women responded by tearing up sheets to cover their faces.

Abu Dawud (32:4092) - The Apostle of Allah... said: "O Asma', when a woman reaches the age of menstruation, it does not suit her that she displays her parts of body except this and this, and he pointed to her face and hands" This was narrated by Aisha.

Abu Dawud (2:641) - The Prophet (peace_be_upon_him) said: Allah does not accept the prayer of a woman who has reached puberty unless she wears a veil.

Sahih Bukhari (52:250) - [The Prophet said] "It is not permissible for a man to be alone with a woman, and no lady should travel except with a Muhram (i.e. her husband or a person whom she cannot marry in any case for ever; e.g. her father, brother, etc.)." - Neither is a woman allowed to travel by herself.

Sahih Muslim (26:5395) - A'isha reported that Sauda went out (in the fields) in order to answer the call of nature even after the time when veil had been prescribed for women*. She had been a bulky lady, significant in height amongst the women, and she could not conceal herself from him who had known her. 'Umar b. Khattab saw her and said: Sauda, by Allah, you cannot conceal from us'.... he said:" Permission has been granted to you that you may go out for your needs."* - This is proof that Muslim women were told by Muhammad to wear the burka, rather than a simple hijab.  Here, a woman who wanted to relieve herself (without first seeking permission from a man) was identifed by Umar by her height rather than her face, since it would not have been visible.