The club made the announcement in a release Saturday night without providing additional details.
The team thanked Mellanby, while also indicating it would not comment further.
Mellanby joined the Canadiens as director of player personnel in 2012. He was promoted to assistant general manager under current general manager Marc Bergevin in 2014.
Mellanby played 21 seasons in the NHL with the Philadelphia Flyers, Edmonton Oilers, Florida Panthers, St. Louis Blues and Atlanta Thrashers. He had 840 points in 1,431 games. He retired in 2007. Mellanby this month played in a Flyers alumni game in Philadelphia.
It's been a tough season for the Canadiens, who have endured a lot of roster turnover to coincide with a sluggish start. After advancing to the Stanley Cup Finals, where they lost to the Tampa Bay Lightning, last season, Montreal, which defeated the Pittsburgh Penguins, 6-3, on Saturday night, is just 6-15-2, and one step from last place in the Atlantic Division.
Among the most glaring problems that Montreal has had on the ice, is on the blue line. The defense has struggled to gain rhythm, and through Saturday, the Canadiens had allowed 83 goals, most of any team in the Eastern Conference.
The Associated Press contributed to this report.