The request comes after a banana was tossed at Hurricanes goaltender Kevin Weekes, who is black.
Canadiens spokesman Donald Beauchamp said the club "does not tolerate such behaviour and if members of our security staff witness such actions, they will react promptly."
The banana was thrown onto the ice as the players went to the dressing room following Montreal's 2-1 overtime victory over Carolina in Game 3 of their best-of-seven NHL playoff series on Tuesday night.
It ended up on the ice near one of the blue lines, where Carolina defenceman Aaron Ward pointed it out to linesman Ray Scapinello.
"We brought it to the attention of the league, but Kevin just wants to let it go, so we're willing to do that," Hurricanes general manager Jim Rutherford told the Raleigh News-Observer.
"We don't hold the Canadiens responsible for the behaviour of a fan."
Neither Weekes nor his teammates had any comment on the incident.