Also let go was fellow assistant coach Randy Ladouceur, General Manager Marc Bergevin said.
Cunneyworth's Dec. 17 choice as the interim replacement for the fired Jacques Martin brought protests from fans and others because he was not a French speaker.
The Habs stumbled to an 18-23-9 under Cunneyworth's guidance and missed the playoffs.
Michel Therrien was tabbed as Montreal's new head coach Tuesday.
"Following my appointment as head coach of the Montreal Canadiens, I made the decision of bringing together a new coaching staff," Therrien said. "Out of respect for Randy Cunneyworth and Randy Ladouceur, I felt it was important that I notify them immediately in order for them to start looking for other opportunities without further delay."