Bavuma as well as fast bowler Kagiso Rabada will play no part in the limited overs series in order to prepare for two World Test Championship matches, starting in Centurion on December 26.
Fast bowlers Gerald Coetzee, Lungi Ngidi and Marco Jansen will only play in the first two T20 internationals before returning to their franchises to play in domestic four-day cricket ahead of the Test series.
One-day coach Rob Walter said the decision was made in consultation with Test coach Shukri Conrad.
"We have a busy summer ahead starting with the T20Is and then ODIs against India and we have therefore taken the decision to omit several of our senior players," said Walter.
"This decision was taken together with coach Shukri as we place emphasis on the red-ball leg of the tour, meaning they will instead be preparing for the Test series by playing domestic cricket."
Conrad said: "It is the start of a new ICC World Test Championship cycle and that itself is a huge incentive for everyone. We want to try and ensure we make a strong start to this sequence here at home against one of the best teams in the world."
The Test squad includes three uncapped players in Durham and Western Province batsman David Bedingham, left-arm fast bowler Nandre Burger and batsman Tristan Stubbs.
Burger is set to make his international debut after being named in all three squads. Another newcomer is all-rounder Mihlali Mpongwana, who was selected for the one-day series.
The first T20 international will be played in Durban on Sunday. There will be three T20 internationals and three one-day internationals.
India will also be without key players for the white-ball matches, with regular captain Rohit Sharma and former captain Virat Kohli rested ahead of the Test matches.
South African squads:
T20 internationals: Aiden Markram (captain), Ottniel Baartman, Matthew Breetzke, Nandre Burger, Gerald Coetzee, Donovan Ferreira, Reeza Hendricks, Marco Jansen, Heinrich Klaasen (wkt), David Miller, Lungi Ngidi, Andile Phehlukwayo, Tabraiz Shamsi, Tristan Stubbs, Lizaad Williams
One-day internationals: Aiden Markram (captain), Ottniel Baartman, Matthew Breetzke, Nandre Burger, Tony de Zorzi, Reeza Hendricks, Heinrich Klaasen (wkt), Keshav Maharaj, Mihlali Mpongwana, David Miller, Wiaan Mulder, Andile Phehlukwayo, Tabraiz Shamsi, Rassie van der Dussen, Kyle Verreynne (wkt), Lizaad Williams
Tests: Temba Bavuma (captain), David Bedingham, Nandre Burger, Gerald Coetzee, Tony de Zorzi, Dean Elgar, Marco Jansen, Keshav Maharaj, Aiden Markram, Wiaan Mulder, Lungi Ngidi, Keegan Petersen, Kagiso Rabada, Tristan Stubbs, Kyle Verreynne (wkt)
Fixtures:
December 10, first T20 international, Durban
December 12, second T20 international, Gqeberha
December 14, third T20 int6ernational, Johannesburg
December 17, first one-day international, Johannesburg
December 19, second one-day international, Gqeberha
December 21, third one-day international, Paarl
December 26-30, first Test match, Centurion
January 3-7, second Test match, Cape Town
