“And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what must ordinarily appear therof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husbands’ fathers, their sons, their husbands’ sons, their brothers, or their brothers’ sons or their sisters’ sons, or their women or the servants whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex, and that they should not strike their feet in order to draw attention to their hidden ornaments. And O you Believers, turn you all together towards Allah, that you may attain Bliss.” (Quran 24:31).
“O Prophet, tell your wives and your daughters and the women of the believers to draw their cloaks close round them (when they go abroad). That will be better, so that they may be recognised and not annoyed. Allah is ever Forgiving, Merciful.” (Quran 33:59)
The Prophet Muhammad (peace be upon him) told women to cover.
Narrated Aisha, Ummul Mu'minin:
Asma (r.a.), daughter of AbuBakr (r.a.), entered upon the Messenger of Allah (s.a.w.) wearing thin clothes. The Messenger of Allah (s.a.w.) turned his attention from her. He 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. (Abu Dawud Book 32, Number 4092)
Covering the face
The niqaab is the face covering that lots of Muslim women wear. There is lots of evidence that the early Muslim women used to cover their faces. Many scholars believe that it is compulsory for Muslim women to cover their faces, and others believe it is recommended but not compulsory.
Narrated Safiya bint Shaiba (r.a) "Aisha (r.a) used to say: "When (the Verse): "They should draw their veils over their necks and bosoms," was revealed, (the ladies) cut their waist sheets at the edges and covered their faces with the cut pieces. (Sahih Al-Bukhari Volume 6, Book 60, Hadith # 282)
Narrated 'Aisha (r.a.) The Messenger of Allah (s.a.w) used to offer the Fajr prayer and some believing women covered with their veiling sheets used to attend the Fajr prayer with him and then they would return to their homes unrecognized . (Sahih Al-Bukhari Volume 1, Book 8, Hadith # 368 )