Gibson was injured in a game against New Jersey on March 19. After consulting with an outside specialist, the Cavs' team doctors decided on the operation, which will likely end Gibson's season.
The Cavs said Monday that a timetable for Gibson's recovery will be updated following a "post-operative review."
Gibson had an injury-plagued season, his sixth in the NBA. He averaged 7.5 points in 35 games -- 7 starts -- but shot a career-low 35 percent from the floor. The 26-year-old has been with the Cavs since 2006, when he was selected in the second round. He is under contract for one more season.