The South African Rugby Union had said earlier this week they expected the 32-year-old, who limped out of the 55-6 victory over Scotland on Saturday, to be sidelined for three months.
However medical advice after surgery suggested it would take twice as long as initially thought to recover.
"It's a massive blow to lose yet another world class player and a key player due to an injury," Springbok coach Heyneke Meyer said.
"Fourie has been brilliant since he returned to the Springboks last year and he will be missed. However, this provides an opportunity for other scrumhalves to prove themselves and make the step up when the opportunity arises."
South Africa, who finished second behind New Zealand in last year's Rugby Championship, begin their 2014 campaign at home to Argentina on Aug. 16.
(Reporting by Nick Said; editing by Josh Reich)
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