A replacement for Gauthier, who was promoted to the job in February 2010, has not been named.
The Canadiens made the NHL playoffs in Gauthier's first full season in charge but were eliminated by the eventual Stanley Cup champion Boston Bruins in the opening round last year.
The team took a backwards step this season and are currently sitting in last place in the Eastern Conference standings with five regular seasons to go.
Montreal (29-34-14) were eliminated from playoff contention when they lost to the Philadelphia Flyers on Saturday.
Gauthier, who joined the organisation as Director of Professional Scouting in 2003, had a controversial 2011-12 season during which he fired the team's coach.
He was heavily criticised by many French-speaking fans of the Canadiens when he appointed English-speaking Randy Cunneyworth as Jacques Martin's replacement on an interim basis.
The Canadiens have won the Stanley Cup a record 24 times but not since 1993.