The 28-year-old's ongoing injury problem is a blow as he had been expected to compete for a place in the Australian top order, which is under intense scrutiny after Monday's first test defeat to New Zealand since 1993.
Marsh, who scored a century on his test debut in Sri Lanka in September, has not played since injuring his back in the first test against South Africa last month, which Australia lost after being skittled for 47 in the second innings.
He had been selected to play for a Chairman's XI in Canberra in India's second tour match, which starts next Monday, but has now been ruled doubtful for the Boxing Day test at the Melbourne Cricket Ground (MCG).
"While we are hopeful, Shaun's chances of recovering sufficiently in order to be considered for the first test against India are unlikely at this stage," Cricket Australia's Pat Howard said.
Ed Cowan, who has been in prolific form with the bat as an opener for Tasmania this year, has been moved from the team for India's first tour match, which starts in Canberra on Thursday, to replace Marsh in the second.
