Hazlewood is expected to miss the final two Tests of the Border-Gavaskar Trophy through a calf strain.
On return from a side strain, the Australian quick was hurt again in the warm up in Brisbane on Tuesday, before bowling one over and leaving the field.
Australian officials on Wednesday defended their decision to pick Hazlewood for the Gabba, adamant he was at no extra risk of another injury.
"Josh passed all assessments before he was selected for the third Test and was fully fit entering the match," high-performance boss Ben Oliver said.
"Unfortunately Josh suffered a new, unrelated calf injury during the warm-up on day four.
"This is disappointing for Josh who does everything right in his preparation and is a highly valued member of the team.
"We have the very best medical staff who will now oversee Josh's rehabilitation from this new injury."
Scott Boland is expected to replace Hazlewood in Melbourne, with the series locked at 1-1 and India needing only one more victory to retain the trophy.
Questions had been asked before the series whether Starc, Cummins or Hazlewood could play through the entire series, without their performances waning.
Pat Cummins has bowled 88 overs so far in the Test series. (Jono Searle/AAP PHOTOS)
But Hazlewood's injury now means it is vital both Starc and Cummins play and perform in Melbourne and Sydney.
With Hazlewood injured, the duo were forced to bowl 48.1 overs of the 81 overs India faced at the Gabba.
Starc has bowled 90.2 overs for the series and Cummins 89.5.
"They are still at the relative numbers we would expect through this amount of Test matches," Australia's bowling coach Dan Vettori said.
"They had a pretty light workload in Adelaide and because of the breaks it didn't feel like we pushed them too hard.
"We tried to push them longer to get India's last wicket (on day four), that was probably the only time we felt they were slightly extended, but otherwise it feels like the norm."
Mitch Marsh's bowling is also likely to become crucial.
Marsh had declared before the Brisbane Test he had overcome back soreness, but was only called on for two overs in India's first innings.
The allrounder may need to be used more in Melbourne as Australia manage their workloads to ensure Starc, Cummins and Boland are all fit for Sydney.
Australian team officials have defended their handling of Josh Hazlewood's fitness. (Jono Searle/AAP PHOTOS)
"He's good to go, there are no issues around his fitness," Vettori said.
"It was just the way the weather delays came that allowed Patty and Mitch (Starc) to keep going.
"He'll be incredibly important part of the next two Tests, particularly Melbourne, I think that is a wicket that suits him.
"And to be able to complement whoever comes into that team, that is when he is at his best."
Australia have carried Beau Webster in their squad as a back-up to Marsh if his back issues return, while quicks Sean Abbott and Brendan Doggett have also acted as reserves.