The WBA recently sanctioned the fight following Peterson's controversial title win in Washington DC last month.
The American claimed the WBA and IBF light-welterweight titles after a points decision.
However, the appearance of a mystery man at ringside prompted Khan to lodge an appeal with the authorities.
The man has since been identified as offical Mustafa Ameen, who claimed to be helping an ill judge with his scorecard.
Khan recently withdrew his appeal with the IBF for unknown reasons.
Khan's withdrawal means that Peterson will keep the IBF belt, but he must defend his WBA title.