Smith — serving a 12-month ban from international cricket for his part in the Cape Town ball-tampering scandal — missed the Tridents' defeat to the St Lucia Stars and would play no further part in the T20 tournament, his team said.
"He had a slight tear and he had to go back, so it's a really unfortunate situation," Tridents captain Robin Singh said.
Joe Root revels in India series win
The injury is not expected to prevent Smith returning to domestic cricket later this month. Although banned from playing for his home state New South Wales (NSW), Smith is scheduled to play for his Sydney club side Sutherland on Sept. 22, Cricket Australia's website (cricket.com.au) said.
Signed as a replacement for Bangladesh's Shakib Al Hasan, Smith scored 185 runs in seven innings for the Tridents and took three wickets in his time there.
His ban ends in March 2019 but he will be suspended from leadership roles for a further 12 months.
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