Primeau, a center who has four goals and nine assists in 38 games this season, was hit by a slap shot from Florida defenseman Jay Bouwmeester late in the first period and immediately left the game.
"The x-ray we all looked at, let it heal a little bit and then whenever he can play, he's probably going to have to play with some type of splint," Flyers Coach Ken Hitchcock said. "It could be three weeks before he's back, so we will just have to go with what we got and move along."
A 14-year veteran who has spent the last five seasons with Philadelphia, Primeau has 262 goals and 603 points in 883 games.
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