Reports emerged late last month that the loose forward, who lifted the Webb Ellis Cup in Japan four years ago, suffered a partial tear to his anterior cruciate ligaments playing for the Sharks against Munster in the United Rugby Championship.
"Kolisi underwent the operation on Friday and Springbok team doctor Jerome Mampane and his medical team will continue to monitor his recovery and rehabilitation," governing body SA Rugby said in a statement.
"Mampane said it was too early to make any reliable forecasts on when Kolisi may be able to return to play."
SA Rugby and Kolisi's club had remained tight-lipped about his condition over the last 10 days. The player's wife Rachel first confirmed the surgery via social media at the weekend.
Kolisi, one of the most respected figures in the game, is due to move to French club Racing 92 after the World Cup, which runs from September 8th to October 28th.
It is now a race against time for him to make the squad for the tournament in France.
"We wish Siya well during his recovery and we know that he will do everything possible to return to play soon as possible," said Springboks coach Jacques Nienaber.
South Africa, who name their final 33-man squad on August 8th, begin their title defence against Scotland in Marseille on September 10th.
