Dale Steyn has fully recovered from a shoulder injury and recently featured for the Melbourne Stars in Australia's domestic Big Bash league.
Fast bowler Dwaine Pretorius took a record 5-17 in South Africa's six-wicket victory.
He joins injured fast bowler Kagiso Rabada on the sidelines.
The loss of Bavuma will further weaken their top six, especially as the experienced Reeza Hendricks has withdrawn from the squad after the birth of his first child, while the in-form Rassie van der Dussen is doubtful for the first match of the series, at least, with a grade one left quadriceps strain.
Led by Quinton de Kock, South Africa's 44 cricketers, who are part of a men's high performance squad, have returned to training amid the COVID-19 pandemic after getting approval from the country's sports ministry. South Africa has reported more than 1,38,000 COVID-19 cases with over 2,400 deaths.
Also included is fast bowler Anrich Nortje, but in-form opening batsman Temba Bavuma will have to prove his fitness after injuring his hamstring against England on Sunday.
India Test regulars like Cheteswar Pujara and Ishant Sharma have also thrown their hat into the ring with base prices of Rs 50 and Rs 75 lakh respectively.