Cricket South Africa (CSA) said Rabada had suffered a right hamstring strain and would miss the three ODIs starting September 24 in Durban.
"His availability for the three-match test series against Australia will depend on how he progresses through his rehabilitation, with a decision on his selection to be made closer to the series," CSA said in a statement.
Rabada's domestic bowling coach Allan Donald told South African media Rabada's hamstring injury could see him sidelined for up to 10 weeks.
The first test starts on October 9 in Durban, with Gqeberha and Cape Town also hosting matches.
Losing Rabada for the test series would be a huge blow for South Africa, who beat Australia in the World Test Championship final at Lord's last year when the 31-year-old took nine wickets.
Rabada has an average of 21.39 in 11 tests against Australia, slightly better than his exceptional career average of 22.03.