Wicketkeeper Brad Haddin is expected to assume the test captaincy.
Australia called on West Australian batsman Marsh and also added left-arm paceman Mitchell Starc to their squad for the Gabba test.
Clarke was passed fit to play the series opener which Australia won by 48 runs after overcoming a left hamstring strain suffered in a one-day match on November 14.
But he suffered a recurrence of his long-term back injury while batting on Tuesday's opening day which forced him to retire hurt.
Clarke had injections to soothe spasms in his back and returned to the crease the next day to complete a century.
But he was injured again when fielding a ball in India's second innings on Saturday.
Clarke collected a ball in his left hand and shaped to throw but didn't release the ball, instantly pulling up lame.
He limped from the field accompanied by Australian team physiotherapist Alex Kountouris and briefly grabbed his right hamstring while exiting.
After Clarke suffered his back injury, Kountouris described it as "significant".
Clarke has three degenerative discs in his lower back which were first diagnosed when he was aged 17.
"This is his right lower back. This is his old injury, what he's had in the past," Kountouris said on Wednesday.
"I don't think it's directly related to his (left) hamstring (strain) because it's the other side.
"We believe it's related to his old disc injuries. With that comes a lot of muscle spasms and other things that cause pain."
-AAP