Hazlewood sent down just one over on Tuesday morning before exiting and leaving Australia a bowler short for the rest of the match, with 13 wickets still to take in the match for victory.
Officials fear the quick will miss the rest of the series, with Scott Boland the front-runner to replace him in both Melbourne and Sydney.
It also came as large chunks of the first two sessions were washed out, with Australia racing the rain to try and take a 2-1 series lead with two Tests to play.
The fate of India's innings now firmly sits with Ravindra Jadeja, with the allrounder not out on 65 alongside tailender Mohammed Siraj when another rain delay forced tea to be called.
Josh Hazlewood in action on day four at the Gabba before leaving the field with injury. (Jono Searle/AAP PHOTOS)
Australia claimed two first-session wickets and another in the brief period of play before tea, with the moment of the day a one-handed blinder from Steve Smith to remove KL Rahul on 84.
But it was a chance Smith missed on the first ball of the day that Australia could rue.
Rahul edged a Pat Cummins delivery straight to Smith at second slip, only for Australia's vice-captain to spill the opportunity.
The right-hander then added 55 more runs and soaked up an extra 75 balls, before offering Smith a far harder chance off Nathan Lyon.
Going back to cut, Rahul hit the ball with force only for Smith to dive one handed to his right and take the catch at slip.
The wicket broke a 67-run sixth-wicket stand between Rahul and Jadeja, who went to the lunch break unbeaten on 41.
WHAT A CATCH FROM STEVE SMITH!— cricket.com.au (@cricketcomau) Sweet redemption after dropping KL Rahul on the first ball of the day.#AUSvIND | #PlayOfTheDay | @nrmainsurance pic.twitter.com/d7hHxvAsMdDecember 17, 2024
Jadeja then combined with Nitish Kumar Reddy for another 53-run stand, before he chopped on from Cummins before tea for 16.
Australia's only other wicket on Tuesday came when Cummins (3-49) had out-of-form India captain Rohit Sharma caught behind for 10.
Further rain is forecast for Brisbane on Wednesday, meaning Australia have a steep hill to climb to claim victory in the Test.
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