The 19-year-old forward, in his second season, has 10 goals and 13 assists in 44 games. As a rookie, he had 27 points in 48 games, and one goal and two assists in five Stanley Cup Playoff games.
Galchenyuk appeared to be injured midway through the first period when he was checked by Panthers defenseman Mike Weaver along the boards. Galchenyuk played one more shift before he went to the dressing room late in the first, but returned for the beginning of the second period and finished the game.
"It's bad news for us and for Alex too," Montreal coach Michel Therrien said Tuesday. "It happened [Monday] and he's going to be out 4-6 weeks. He finished the game, a lot of courage, and when they passed the MRI they found out it was a small fracture, so he'll be out."
The third pick of the 2012 NHL Draft, Galchenyuk has 19 goals and 50 points in 92 games. He also won a gold medal with the United States at the 2013 IIHF World Junior Championship and had two goals in four games for the U.S. at the 2013 World Championship.
Canadiens goalie Carey Price learned of Galchenyuk's injury during Montreal's practice on Tuesday.
"He's an important player on our hockey club," Price said. "He's very talented offensively. He contributes a lot to our team. Whenever you lose a guy on your team it hurts, and I hope he can recover quickly and I'm sure he'll be highly motivated when he gets back."