It is believed Smith, who was leading the Comilla franchisee in the first two games, aggravated an old injury. In the two matches he played for the Comilla Victorians, he scored 16 and a duck.
The operation is a major blow to Smith, whose 12-month suspension for his involvement in the ball-tampering scandal ends on March 28.
Smith might end up missing the Indian Premier League (IPL) and the Pakistan Super League (PSL) due to the elbow surgery. Smith was retained by Rajasthan Royals for this season of IPL. Meanwhile, in PSL he has signed up to play for Multan Sultans.