Cricket Australia said Smith had laboured due to pain in his right wrist for the past week while playing for Pune in the Twenty20 tournament.
"From the information we have so far, this doesn’t appear to be a serious injury but we are keen to give him the time to recover and rehabilitate before heading to the West Indies at the end of May,” CA said in a statement on Monday.
All-rounder Mitchell Marsh was also pulled from the IPL to have treatment on a side strain, CA had said on Sunday.
Australia will play a one-day international tournament with West Indies and South Africa in June.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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