Steyn is set to need up to four weeks to recover from the injury which he sustained while fielding on the opening day of the 10-wicket win over India in Durban.
The 30-year-old was able to finish the Test, and ended up with nine wickets in the victory, but a scan after the match revealed the extent of the problem and he has now been given a rehabilitation programme.
That means Steyn is no longer available to play for the Cape Cobras in the current T20 competition, but South Africa believe he will be fine to face Australia in the first Test, which is scheduled to begin in Centurion on February 12.
South Africa team manager Dr Mohammed Moosajee said: "Dale dived while fielding a ball on day one of the second Test against India in Durban and complained of slight pain of his right anterior chest region.
"He continued playing and bowling with mild discomfort for the rest of the Test. When the discomfort persisted after the Test match, a scan was performed which detected a small undisplaced fracture to his right eighth rib.
"He will follow a strict rest and rehabilitation programme for the next three to four weeks and we are confident he will be fit for the tour against Australia."
Steyn was recently replaced by team-mate Vernon Philander at the top of the ICC Test bowling rankings having held first place since July 2009.
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