Saha, who is not part of the team playing the ongoing second Test here, picked up the injury while training on January 11.
The third and final Test of the series is scheduled to be held in Johannesburg from January 24.
"The All-India Senior Selection Committee has named Dinesh Karthik as the replacement for Wriddhiman Saha for the third and final Test against South Africa. He is set to join the team before the third Test," the BCCI Acting Secretary Amitabh Choudhary said in a statement.
"Mr. Wriddhiman Saha suffered an upper left hamstring tendon injury during training on Thursday, January 11. The BCCI Medical Team will continue to monitor his progress," Choudhary said.
Saha was replaced by Parthiv Patel in the ongoing Test here after he picked up the injury, which was initially described as a niggle.
He wasn't much of a success in the opening Test in Cape Town, returning scores of 0 and 8. But the 33-year-old broke Mahendra Singh Dhoni's record for most dismissals by an Indian wicketkeeper in a Test match.
Since making his debut against South Africa in 2010, Saha has represented India in 32 Tests, effecting 85 dismissals - 75 catches and 10 stumpings.
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