The development comes close on the heels of South Africa losing Vernon Philander due to multiple ligament injuries in his left ankle.
Steyn was ruled out after he failed to recover fully from a groin injury suffered during the first Test in Mohali.
"Obviously losing Dale, the best bowler in the world, and Vernon, arguably the best all-rounder in the world, certainly changes the dynamics of the side," South Africa skipper Hashim Amla told reporters before their net practice at Chinnaswamy stadium today.
However, Amla was hopeful of Steyn recovering in time for the next Test to be played at Nagpur beginning November 25.
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"I am hopeful Steyn will recover well on time for the third Test at Nagpur," he said.
Cricket South Africa, soon after Philander was ruled out of rest of the series due to multiple ligament injuries in his left ankle, flown in Kyle Abbott as replacement.
Replying to a query, Amla said that Abbott could replace the injured Steyn.
Replying to a query on players who would be replacing Steyn and Philander, Amla said, "The guys who are going to be replacing them are quality cricketers. We are fortunate that we have great depth in our bowling especially. If you are going to win a Test series, the series is won with 15 players usually, not just 11. Although it's early in the series, I still think we have a potent attack to back it up.