Kohli damaged his right shoulder when diving to save a boundary on the first day of the penultimate test in Ranchi and was off the field during most of Australia's first innings in the drawn game.
The 28-year-old did come out to bat at his usual number four position and took the field for Australia's second innings. There is no suggestion he has yet been ruled out of the winner-takes-all fourth test in Dharamsala.
"Shreyas Iyer is joining the squad as back-up," an Indian cricket board (BCCI) source told Reuters.
India's batting mainstay Kohli has scored only 46 runs in his five innings against Australia after scoring a double century in each of the previous four series.
The decision to call up Iyer has more to do with the difficulty involved in flying out a last-minute replacement to Dharamsala, which is situated in the Himalayan foothills.
Iyer, 22, was Mumbai's highest scoring batsman in the 2016-17 Ranji Trophy and struck an unbeaten 202 in a first-class match for India A against Australia last month.
The four-match series is level at 1-1 going into the decider which starts on Saturday.
(Reporting by Simon Jennings and Sudipto Ganguly, editing by Ed Osmond)
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