South Africa are scheduled to face Australia in three ODIs from September 24 to 30 on home soil. Rabada will miss the series as he begins his recovery from the injury.
The two teams will then meet in a three-match Test series, starting on October 9. Rabada has less than six weeks to recover before the opening Test.
Cricket South Africa (CSA) said Rabada will be sidelined for at least four and a half weeks, although the board did not disclose the exact severity of the injury.
His absence from the ODI series is therefore confirmed, while his participation in the Test series will depend on his rehabilitation progress.
CSA said a decision on his availability will be made closer to the start of the Test series.
