Bavuma sustained the injury while batting during South Africas second innings on day three of the ICC World Test Championship Final against Australia at Lords Cricket Ground.
He is set to undergo further scans to assess the extent of the injury.
Keshav Maharaj will captain the side in his absence.
The squad will depart for Bulawayo on Tuesday, 24 June from OR Tambo International Airp
The first Test gets underway on Saturday, 28 June, followed by the second Test from Sunday, 6 July, with both matches taking place at Queens Sports Club.
Even without Bavuma, the Proteas are expected to be far too strong for Zimbabwe.
Keshav Maharaj captain, Hollywoodbets Dolphins, David Bedingham Western Province, Matthew Breetzke Warriors, Dewald Brevis Titans, Corbin Bosch Titans, Tony de Zorzi Western Province, Zubayr Hamza Lions, Kwena Maphaka Lions, Wiaan Mulder Lions, Lungi Ngidi Titans, Lhuan-dr Pretorius Titans, Lesego Senokwane Titans, Prenelan Subrayen Hollywoodbets Dolphins, Kyle Verreynne Western Province, Codi Yusuf Lions