Steyn was injured two weeks ago while fielding in the second test against India but played on to take nine wickets as South Africa claimed a series win with a 10-wicket victory.
"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," Proteas team manager Dr Mohammed Moosajee said in a CSA statement.
"He continued playing and bowling with mild discomfort for the rest of the test. When the discomfort persisted after the 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's injury is likely to rule him out of entire domestic Twenty20 competition, where he would have turned out for the Cape Town-based Cobras. South Africa will play three tests and three Twenty20 internationals against Australia, starting with the first test in Centurion on Feb. 12.
(Reporting by Nick Said,; editing by Pritha Sarkar)