In countries on the Arabian Peninsula, this garment is known as an abaya. The abaya is typically black, and it drapes from the head or the shoulders down to the feet.n Saudi Arabia, where it is a law that women must cover themselves, the abaya is worn with the niqab, a veil that covers all parts of the head and face except for the eyes. The muttawa, or religious police, enforce the law and may punish a woman if she is seen without this covering.