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.
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