The 29-year-old Bavuma got injured while fielding in the third T20I against England on Sunday.
The recommended recovery time for the Bavuma's injury is seven to 10 days.
The right-hand batsman will remain with the team and receive treatment from the medical staff in the hopes of returning to play in time for the second T20I match in Port Elizabeth.
No replacement will be called into the squad. The Proteas will face Australia in the first T20I of the three-match series on February 21.
Earlier on Monday, Faf du Plessis stepped down as the skipper of South Africa's Test and T20I teams. However, the 35-year-old will remain with the squad for the upcoming T20I series against Australia.