Mkhwebane, who assumed her post in October last year, has made several controversial decisions and proposals since she took over from the well-respected Thuli Madonsela.
She dropped a bombshell when she ordered parliament to change the Reserve Bank's mandate as part of her remedial action over the controversial Absa/Bankorp report.
The order was deemed to be a remarkable breach of the constitutionally enshrined doctrine of the separation of powers - which prohibits the three arms of state from interfering with one another.
ANC MP and justice committee chairman Mathole Motshekga said he would recuse himself from the process that could see Mkhwebane being removed before her term expired.
Motshekga proposed that the matter be sent back to Mbete for parliament to set up an ad hoc committee to look into the matter, but the justice committee insisted that it was the correct body to decide her fate.