Hill, who has been troubled by the injury since the beginning of the season, is expected to be sidelined for about six weeks after the surgery.
"Although Clint has been playing, he has been struggling and we have identified a little spur of bone around the ankle joint which needs to be removed," Stoke manager Tony Pulis told the clubs website.
"He is going to have surgery immediately and at the moment we are looking at up to six weeks before he will be ready to play again."