Fast bowler Josh Hazlewood will take no further part in Australia's increasingly ill-fated tour of India and will return home after failing to recover from an Achilles injury, the team said on Monday.

Captain Pat Cummins will also be returning to Australia due to a serious family illness but will be back in time for the third Test starting in Indore on March 1.

Opening batsman David Warner, who suffered a concussion and a fractured arm after being hit by the ball while batting in the second Test, will remain with the squad.

Any changes to the squad will be announced on Wednesday once the selectors and medical staff have deliberated, a team spokesman said.

Head coach Andrew McDonald said they would also be in touch with Cummins.

"We've got some decisions to make around squads and injuries as they unfold," McDonald told reporters.

"So he'll still be engaged in those conversations whilst dealing with what's happening back home."

Australia are 2-0 down in the four-test series after being thrashed by six wickets in the second match in Delhi on Sunday and by an innings and 132 runs in the opener in Nagpur.

Hazlewood missed the first two Tests because of the injury he sustained in the third test against South Africa in Sydney in January.

His fellow quick Mitchell Starc and all-rounder Cameron Green also missed the first two matches as both recovered from broken fingers.

McDonald said Green would be available for the next match while Starc was progressing well.

"Starc was available for the last game, but was he fully fit? That's another question. Is he fully fit for this game? He's closer," McDonald added.

He said spinner Todd Murphy had a slight niggle in his side but was not in danger of missing the next match.

"He'll have... not a test but a good workout two days before," McDonald said. "He needs a break so you won't see him doing much work... but it looks good."