The pace spearhead will return home to begin his rehabilitation, Cricket Australia said in a statement on Friday.
"Mitchell experienced some pain in his right foot during the second test in Bangalore which unfortunately had not subsided a few days after the test as we had hoped," team physiotherapist David Beakley said.
"We made the decision to scan his foot in Bangalore this morning and unfortunately it has revealed a stress fracture.
"Subsequently, this means Mitchell will be unavailable for the remainder of the Qantas tour of India and will return home to Australia to start his rehabilitation."
The left-armer, known for his blistering pace and ability to swing both the old and the new ball, took five wickets in the first two tests and also contributed handsomely with the bat in Australia's 333-run win in the series opener in Pune.
The 27-year-old, who has a history of injury problems, joins Mitchell Marsh on the sidelines after the all-rounder was ruled out of the matches in Ranchi, beginning on Thursday, and Dharamsala with a shoulder problem.
"The National Selection Panel will confirm a replacement player in due course," said Cricket Australia, who have named Marcus Stoinis as Marsh's replacement.
Jackson Bird is the reserve fast bowler in the Australia squad but was not selected for the first two matches.
(Reporting by Sudipto Ganguly; Editing by John O'Brien and Nick Mulvenney)
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