The PSL's top scorer, with 10 goals in 2013/14, has been ruled out for three to four months, meaning he will miss the start of the coming season.
The Bafana Bafana regular, who battled with the knock for much of the past campaign, will spend the next six weeks in a 'moon-boot', after which he will begin his rehabilitation.
Chiefs' team physio Dave Milner explained Parker's situation on the club's website: "Parker has undergone surgery on his ankle. The PSL’s 2013/14 Top Goal Scorer battled throughout the season with a troubling ankle injury which led to the medical team deciding to carry out the surgery sooner than later.
"We expect Parker to be fully recovered in three to four months which means he will miss the start of the 2014/15 season."