The two-year veteran was injured Wednesday in the Cavaliers' 96-89 loss to Boston in game 5 of their Eastern Conference semifinal series.
The injury likely will end Gibson's season.
"It's not good seeing a guy that key to your team in a suit," Cavaliers' forward LeBron James told the Columbus (Ohio) Times Dispatch after Thursday's practice. "A guy who hasn't played much minutes is probably going to have to step up."
Gibson was averaging 9 points and 2.5 assists in 11 post-season contests.
Game 6 will be played Friday night at Cleveland's Quicken Loans Arena.
The Celtics lead the series 3-2.
If a seventh game is necessary, it will be played Sunday at Boston's Fleet Center.