David Warner could miss the rest of the series after suffering a concussion and hairline fracture to his left elbow during the Delhi defeat. Captain Pat Cummins has also flown home but is scheduled to return for the third Test
Australia will be without Josh Hazlewood for the remaining two India Tests.
The 32-year-old missed the defeats in Nagpur and Delhi with an Achilles problem suffered during the South Africa series.
Hazlewood has been ramping up his rehabilitation in recent weeks but that will now continue at home in Sydney.
David Warner's future participation in the series is in jeopardy after he suffered two injuries during the six-wicket drubbing in the second Test, which ensured India retain the Border-Gavaskar Trophy.
He was removed from the Test after day one with a concussion after being struck by Mohammed Siraj, having previously suffered a hairline fracture in his left elbow having been hit earlier by the India quick.
Warner was substituted out of the Test, replacement by Matthew Renshaw, after day one (Robert Cianflone/Getty Images)
Todd Murphy is also managing a side injury but Australia are optimistic it will clear up by the time the third Test gets underway in Indore on March 1.
"Josh Hazlewood out, he'll be going home," said head coach Andrew McDonald.
"[Warner]'s still sore at the moment. We had a meeting just before discussing through this. We're in no rush to make any decisions at this point in time around Davey. Just seeing how that settles, how functional that is.
"It will be basically how sore and how functional it is as to what decision we make with him and then the length of the injury. There's some talk the length of injury could be anywhere between a week plus depending how that settles down.
"There's a bit of unknown there. I'll leave that to the medical team and they'll inform me once they know."
Cummins has flown home but is expected to play the third and fourth Tests (Robert Cianflone/Getty Images)
On Murphy, McDonald added: "He had a slight niggle in the side.
"It looks as though the timeframe between now and the next Test should be enough to resolve that.
"So he'll not have a test but a good workout two days before. It looks good."
Captain Pat Cummins has flown home due to a serious family illness but is expected to return in time for the concluding Tests of the series.
There is also good news regarding Cameron Green and Mitchell Starc, who are both in contention for the Indore Test.
Green is braced to return to the fold (Robert Cianflone/Getty Images)
Finger injuries have kept both on the sidelines for the first half of the series, though both were close to recalls in Delhi.
Australia went with one seamer - Cummins - and three spinners in Nathan Lyon, Murphy and Matthew Kuhnemann, but may choose to readdress that balance.
The return to fitness of Green and Starc could lead to several unused members of the squad returning home permanently to play domestic cricket.
"We're working through that," added McDonald. "It won't be form as such but there's cricket going on back home.
"And with a few players now becoming fit and available, are we carrying too many? That's probably a question. So we've got to be clear on what we want to achieve in the next two Test matches in terms of the structure of the team.
"Once we get our heads around that, there's an opportunity for players to be playing cricket back home and we value that."
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