Cricket Australia medical official Alex Kountouris said Smith had been struggling with pain in his right wrist for the last week.
“We have been working with his IPL franchise Pune to monitor this and unfortunately it has not resolved,” Kountouris said in a statement.
“As such, he will return home from India for further assessment and treatment ahead of the tour of the West Indies.”
He stressed the injury did not appear to be serious, “but we are keen to give him the time to recover and rehabilitate before heading to the West Indies at the end of May”.
Australia begin the tri-series in Guyana on June 6 against South Africa before facing the hosts four days later at the same venue.
The round-robin tournament sees teams play three matches against each opponent, with the top two advancing to the final on June 26 in Barbados.
Smith’s decision comes a day after Australian all-rounder Mitchell Marsh pulled out of the rest of the IPL with a side strain.