The inspirational Kolisi suffered knee ligament damage on April 22 when his Sharks team played Munster in Durban.
Medical advice was sought on his injury, and he was faced with two choices, have an operation which could potentially keep him out of action for up to nine months, meaning he could miss the World Cup, or have rehabilitation in the hope the injury would heal before the Cup.
Last week he decided to have surgery, and there is a slim chance he could be fit for the World Cup.
South Africa Rugby stated after his surgery.
"Springbok team doctor Jerome Mampane and his medical team will continue to monitor his recovery and rehabilitation. Mampane said it was too early to make any reliable forecasts on when Kolisi may be able to return to play."
Springbok coach Jacques Nienaber said, "We wish Siya well during his recovery, and we know that he will do everything possible to return to play as soon as possible."
South African players not involved in European club playoffs will participate in two training camps later this month. The Springboks are preparing for their Rugby Championship campaign, which opens in Pretoria with Loftus Versfeld already sold out for their game against Australia.
Kolisi and lock Eben Etzebeth, whose shoulder injury means he is unlikely to be ready to play until the Springboks game in Auckland against the All Blacks on July 15, have been invited to attend the first camp to get their on-and-off-field structures organised for the Test season.