Gibson, one of the Cavs' best perimeter shooters, left in pain early in the fourth quarter Wednesday night following a collision and did not return.
The team said an MRI revealed a first-degree separation and estimated he would miss one or two weeks.
The Cavaliers trail 3-2 in the best-of-seven series and face possible elimination on Friday night. They'll miss Gibson, who emerged as a star Game 6 of last year's Eastern Conference finals when he made five 3-pointers and scored 31 points -- 25 in the second half -- as the Cavaliers closed out the Detroit Pistons.
"We know it's a win-or-go-home situation. We've got to approach it that way," LeBron James said after Wednesday night's loss. "We're a very good team at home. But a LeBron James team is never desperate."