Hazlewood is expected to miss the final two Tests of the Border-Gavaskar Trophy through a calf strain suffered during the warm-up on day four in Brisbane.
The Australian quick managed to send down one over early on Tuesday, but left the field afterwards and did not return as India went to stumps at 9-252, having avoided the follow-on .
Scott Boland is expected to replace him in Melbourne, with the series likely to be locked at 1-1 and India needing only one more victory to retain the trophy.
Questions had been asked before the series whether any of Starc, Cummins or Hazlewood could play through the entire series, without their performances waning late.
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 44.5 overs between them amid rain delays by the end of day four in Brisbane.
Starc has also now bowled 89.1 overs for the series and Cummins 87.3.
"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, 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 now.
The bowling exploits of Mitchell Marsh (l) becomes more important now with Josh Hazlewood's injury. (Jono Searle/AAP PHOTOS)
Marsh had declared before the Brisbane Test he had overcome back soreness, but was only called upon for two overs in India's first innings at the Gabba.
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.
"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.
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