Both players are out indefinitely.
Coach Claude Julien said Drouin, 24, will have wrist surgery Monday. He was hurt in Friday's 5-2 win over the Capitals -- taking a big hit from Alex Ovechkin in the second period but then returning in the third. Julien said the injury happened in the third period but was related to the hit.
Byron was also hurt Friday and will have surgery Tuesday. The 30-year-old has a goal and three assists in 19 games this season.
Drouin is fourth on the team with 15 points in 19 games.
The Canadiens are currently second in the Atlantic Division with 26 points, just three behind Boston.
The team recalled forward Charles Hudon from Laval of the AHL.