The 19-year-old suffered the injury in the second period of Montreal's 2-1 victory over Florida on Monday night.
Galchenyuk is fourth in team scoring this season with 23 points in 44 games on 10 goals and 13 points.
The sophomore forward also has posted a minus-7 rating while averaging 14 minutes 42 seconds of ice time.
Galchenyuk was disappointed last week when he wasn't named to the U.S. Olympic team that will compete in Sochi, Russia next month.
"I'm only 19 years old and I'll get other chances," he told reporters. "It's not like I'm killing myself over this."
The Canadiens entered play Tuesday second to Boston in the Eastern Conference's Atlantic Division with a 25-14-5 record.