Team physio David Beakley said Starc had felt pain in his right foot during Australia's 75-run defeat in the the second Test in Bangalore.
"We made the decision to scan his foot in Bangalore and unfortunately it has revealed a stress fracture," Beakley said.
Starc, 27, is one of the world's leading all-rounders and he is the second Australian to be ruled out of the series between the world's top two sides. Mitchell Marsh had to return home with an injured shoulder.
Starc has been hampered by injuries during his career but he has emerged as a key player for his side in all formats of the game and is ranked in the world's top 10 in both Test and ODI cricket.
He was also named recently in the International Cricket Council's Test team of the year. Although Starc has only taken five wickets in the first two Tests, his half-century in the first game in Pune proved to be a turning point in the match, which Australia won.
Ahead of the series, Indian captain Virat Kohli singled him out as one the tourists' most dangerous players. "He is a world-class bowler. He has learnt the art of reverse swing and bowling with the old ball as well," said Kohli. "It's amazing to see, the way he has developed his skills."
The four Test series, which resumes next week in Ranchi, has been marred by a row between Kohli and his opposite number Steve Smith which led cricket's governing body, the International Cricket Council, to call a meeting between the pair.