Bavuma, who is also the limited overs captain of the side, will miss the Twenty20 and One-Day International series as well having been their most consistent performer in the longer format over the last year.
The selectors have opted for only two spinners in the squad in Keshav Maharaj and Simon Harmer, who has vast experience of county cricket with Essex.
South Africa have won seven of their last nine Tests over the previous 12 months, including a 2-1 home win over India and a 1-1 draw in New Zealand.
The tourists also named their squads for the limited overs series that will include three games in each format. There are also two T20 matches against Ireland that will be played in Bristol.
Keshav Maharaj and David Miller will lead the ODI and T20 teams respectively, while there is a first call-up in the shorter format for seamer Gerald Coetzee, 21. Batsman Rilee Rossouw, 32, is in the T20 squad for the first time since 2016.
The Test series will be played at Lord’s (Aug 17-21), Old Trafford (Aug 25-29) and The Oval (Sept 8-12) and will be preceded by the limited overs games that start with the first ODI on July 19.
South Africa Test squad:Dean Elgar (captain), Sarel Erwee, Marco Jansen, Simon Harmer, Keshav Maharaj, Aiden Markram, Lungi Ngidi, Anrich Nortje, Duanne Olivier, Keegan Petersen, Kagiso Rabada, Ryan Rickelton, Lutho Sipamla, Rassie van der Dussen, Kyle Verreynne, Khaya Zondo, Glenton Stuurman.
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