How long have Muslim women worn the burqa?

Answer 1
Wearing Burka (that is covering face) is not an Islamic requirement for women dressing and clothing. It is mainly due to historical local clothing traditions and practices that is not denied or required by Islam rules. Islam required for Muslim women clothing is to wear cloth that covers the whole body; including head, hair, and neck but not necessarily covering face and palm hands. That clothing should not be tight and figuring sexy parts and should not be transparent to show what is underneath.

Answer 2
Since the burqa is a garment that has more to do with local customs than Islam, there are a number of places, such as Afghanistan where burqa-wearing preceded the arrival of the Muslims by a few centuries. In other places, the burqa is only now gaining acceptance as a form of headcovering. However, among Muslim women, there was never a time-period when the burqa was the dominant headcovering among pious Muslim women.