General Manager Pierre Gauthier said the move was made after the Canadiens got off to a 13-12-7 start, last in the NHL's Northwest Division but just 2 points out of second place.
"The primary reason is the team wasn't performing as well as it should be in our minds," Gauthier said at a news conference.
Martin -- the ninth-winningest coach in NHL history -- was let go during his third season as the Habs' mentor. The 59-year-old had previously coached the Ottawa Senators for nine years and the Florida Panthers for five years.
Cunneyworth had been an assistant coach with the Canadiens since being promoted from their Hamilton minor-league affiliate last season.
Gauthier also announced Assistant General Manager Larry Carriere will become an assistant coach with the team.