Warner is the latest of the Australian squad to head home from the subcontinent, with paceman Josh Hazlewood (32) ruled out with an Achilles injury and captain Pat Cummins (29) returning due to a serious illness in the family.
Cummins, however, is expected back in India before the third test starts in Indore on March 1.
Lefthander Warner was replaced by concussion replacement Matt Renshaw (26) in New Delhi after being struck on the grille by fast bowler Mohammad Siraj (28).
That came after being hit on the arm by another bouncer during the six-wicket defeat which saw Australia fall 2-0 behind in the four-match series against India.
With Australia 2-0 down in the series, the team on Monday said Warner would remain with the squad but changed tack after further assessment.
"(Warner) will require a period of rehabilitation which will preclude any further involvement in the remainder of the test series," the team said in a statement.
"It is currently anticipated that he will return to India for the three One-Day Internationals which follow the Test Series."
Warner had struggled in India, making a total of 26 runs from his three innings.
Though Renshaw replaced Warner in New Delhi, Travis Head (29) opened the batting for Australia in their second innings.
Australia all-rounder Cameron Green (23) is fit for Indore after missing the first tests while recovering from a finger injury.
Selectors hope fast bowler Mitchell Starc (33) may also be available and fully recovered from his own finger injury.
Spinner Mitchell Swepson (29) is due to return to India and rejoin the squad, having flown home after the first test in Nagpur for the birth of his first child.
