Smith hurt his right shoulder diving in the field during the fifth and final one-day international against India at Nagpur on Sunday, adding injury to the insult of a 4-1 series loss for the visitors.
The board said an MRI scan had ruled out any serious injury and the 28-year-old would be fit for the start of the domestic season and lead Australia against arch-rivals England at home in the Ashes series starting on Nov. 23 in Brisbane.
"Following the (Nagpur) match, he (Smith) complained of shoulder soreness, which has not settled and is restricting his ability to bat and throw," team doctor Richard Saw said.
"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.
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"He will have further investigation upon his return to Australia but we remain confident he will be available for the start of the Sheffield Shield season."
Vice-captain David Warner would lead Australia in the Twenty20 series, while all-rounder Marcus Stoinis would replace Smith in the squad, Cricket Australia added in a statement.
(Reporting by Sudipto Ganguly; Editing by John O'Brien)
