He will be replaced by Kagiso Rabada while Quinton de Kock is likely to return as wicketkeeper, having been dropped for the last five tests, Amla added but said a final decision had still to be to be taken.
England won the opening test by 241 runs at Kingsmead in Durban on Wednesday.
De Kock’s return would take pressure off AB de Villiers, who returned behind the stumps for the Durban test but looked pressured with the burden of extra work.
Kyle Abbott, who reported stiffness in his hamstring on Wednesday, must face a fitness test to determine whether he stays in the side or is replaced by Chris Morris or Hardus Viljoen, neither of whom have played test cricket.
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Steyn hurt his shoulder in the first test and could bowl only 22 balls in the second innings. Rabada only made his debut in November in India and in three tests took two wickets for 111 runs.
South Africa are still reeling after the first test setback and have drafted in former captain Graeme Smith to assist the side with ideas and their psychological approach.
“He was a wonderful captain for and he knows more than most guys how to play test cricket and how to deal with tough times,” explained Amla at a media conference on Friday.
“He had a few crushing defeats early in his career so he is well aware how important it is as a team to reassess and get back to form. That type of experience is invaluable and that’s why we’ve tried to draw on it.”
Smith had been critical of the team’s performance during the first test where he served as a radio and television analyst.
(The story was refiled to remove the typo in 'Kagiso' in the second paragraph)
(Editing by Justin Palmer; mark.gleeson@thomsonreuters.com; +27828257807; Reuters Messaging: Reuters Messaging: mark.gleeson.thomsonreuters.com@reuters.net)
