Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) said: "A woman should pray in three garments: a shift, a head-covering and a waist-wrapper."
It is reported from Sayyidah Umm Salamah (may Allah be pleased with her) that she prayed in a shift and a head-covering, then said: "Hand me the outer wrap."
Something similar is also reported from Sayyidah Aishah (may Allah be pleased with her).
Sayyidah Aishah (may Allah be pleased with her) was asked about the head-covering, and she said: "The head-covering is that which covers the skin and the hair."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3264