All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The prayer of the one who prays while wearing a wig is valid; and he/she does not have to repeat it. Some scholars are of the opinion that wearing a wig is forbidden. Nevertheless, they do not see that the prayer should be repeated, provided that wearing it does not violate any of the conditions of the validity of the prayer such as purity.
The scholars have clearly mentioned that the prayer of the one who wears some thing forbidden, such as a forbidden turban or a forbidden ring, is valid.
Allaah Knows best.