A heavy downpour overnight delayed the start at the Punjab Cricket Association Stadium and, although the rain stopped for a spell in the morning, it began to drizzle again and led to the umpires calling play off in the afternoon.
Australia trail 2-0 the four-match series and with a depleted squad following the one-match bans handed out to James Pattinson, Shane Watson, Usman Khawaja, and Mitchell Johnson because of much-publicised disciplinary issues.
The quartet were told they would not be considered for the Test after the Australia team management opted to punish them for failing to make a presentation on how the side could improve following the heavy defeat in the second Test.
Of the remaining 13 men, wicketkeeper Matthew Wade, who has been struggling with an ankle injury, missed out along with all-rounder Glenn Maxwell.
Brad Haddin replaced Wade while Nathan Lyon, Steve Smith and Mitchell Starc were named in place of Maxwell, Watson and Pattinson.
Captain Michael Clarke, meanwhile, moved up to three in the batting order from his customary position at number five.
India were convincing victors in the opening two Tests, claiming the first by eight wickets in Chennai and and then winning by an innings and 135 runs in Hyderabad.