The 28-year-old injured his knee during Chiefs' penalty shootout victory over Orlando Pirates in the Telkom Knockout semi-finals last week, ruling him out of contention for South Africa's two-legged clash with Angola in the World Cup qualifiers.
Khune will now begin the recovery process, which could last anywhere from four to six weeks.
"Signing out at hospital after a successful surgery this morning. Thank you very much for all the prayers and messages of support," said Khune.