The 28-year-old batsman's injury is a new blow to Australia as they lost the one-day series in India and are preparing for a key Ashes series against England in two months.
They play their first T20 against the Indians in Ranchi on Saturday.
"Smith landed awkwardly on his right shoulder whilst diving in the field during the fifth ODI against India last Sunday," the team doctor Richard Saw said in a statement.
"Subsequently he has had an MRI scan which has excluded serious injury, but we believe the best course of action is for him to not continue to aggravate his shoulder and allow it to recover."
Australia said all-rounder Marcus Stoinis will take Smith's place in the T20 squad for the three-match series and David Warner will captain the side.
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