Following it, the pacer will be missing the Indian Premier League (IPL) where he was bought for Rs 4.2 crores by the Delhi Daredevils.
Rabada had earlier complained of strain in the culminating fourth Test in Johannesburg and bowled only eight overs in Australia's second innings.
South Africa's team manager Mohammad Moosajee informed that a subsequent scan revealed the injury.
"Kagiso has been diagnosed with a lower-back stress reaction which will rule him out of cricket action for up to three months. He will need a month's break from all physical activity before commencing with a rehabilitation programme to get him ready for the series against Sri Lanka in July," ESPNcricinfo quoted Moosajee as saying.
Rabada, the number one Test bolwer in cricket, finished the Australia series with 23 wickets in four Tests. (ANI)