The fine is the maximum amount allowable under the NHL collective bargaining agreement.
The incident occurred during the first period of the Canadiens’ 4-3 loss to the Red Wings on Tuesday night. As Green was making his way behind Detroit’s net with the puck, Cousins cross-checked him into the boards.
Cousins served a two-minute minor for cross-checking.
The Belleville, Ont., native has five goals, 13 points and 10 penalty minutes in 38 games so far this season.