Kartik, 31, who played the last of his eight Tests against the South Africans in November 2004, was on Monday picked in India's 14-man squad for the first two Tests of the three-match series.
But the left-arm spinner suffered a ligament tear in his left ankle while fielding in a domestic one-day match the same day and doctors said he would be out of action for three weeks.
"It is a serious injury and will take a minimum of three weeks to heal," said Bangalore-based surgeon Chetan Rai, who examined Kartik soon after the incident.
Teenage leg-spinner Piyush Chawla, 19, will replace Kartik for the first Test starting in Chennai on March 26 and the second in Ahmedabad from April 3.
Chawla, who was named a stand-by on Monday, will be in line to play his second Test as part of a spin attack that also includes captain Anil Kumble and Harbhajan Singh.
India are already without pace spearheads Zaheer Khan and Ishant Sharma, who have yet to recover from injuries suffered during the recent three-month tour of Australia.
Khan opted out of the series with an ankle injury while in-form Sharma, 19, was ruled out of the opening Test due to toe and finger niggles.
Sharma was the find of the Australian tour, where India lost 2-1 in the four-Test series, but bounced back to win the tri-series finals 2-0 against the hosts.
Wicketkeeper Mahendra Singh Dhoni and off-spinner Harbhajan, included in the Test squad despite minor injuries, have been asked by officials to pass fitness tests on March 21.
Graeme Smith's South Africa arrive in India for the three-week tour on March 22. The Chennai and Ahmedabad Tests will be followed by the final match in Kanpur from April 11.