Television pictures showed the Great Britain international's inappropraite behaviour during Saints' 35-14 victory over Bradford.
The former Bulls player admitted a charge of ungentlemanly conduct after a Rugby Football League disciplinary hearing studied the video evidence from the McAlpine Stadium.
Bulls prop Sam Burgess complained that he had twice been grabbed inappropriately by Pryce.
The three-game ban means Pryce will not be ruled out of the Challenge Cup final at the new Wembley against Catalans Dragons on August 25.
