Smith, who has signed up to play for the PSL’s sixth franchise, Multan Sultans, only in the UAE leg of the event, has been advised at least six weeks rest to recover from the injury.
Smith, whose one-year ban imposed on him by Cricket Australia ends in late March, hurt his elbow while playing for the Comilla Victorians, for whom he turned out in two matches before being forced to return home.
Smith has been advised surgery on the injured elbow.
The Sultans will have to bring someone from the supplementary category in order to replace the Australian.
Questions remain over how many of the foreign signings for the fourth PSL edition will actually travel to Lahore and Karachi for the final leg and final of the tournament in March after the initial matches are held in the UAE.