Anaheim has lost 19 of its last 21 contests and was handed a seventh consecutive defeat Saturday.
"We thank Randy for everything he has done for the organization," Murray said. "Leading the team to a Stanley Cup and three conference final appearances, he has accomplished so much in Anaheim. Difficult decisions need to be made when times are tough, and our play has clearly been unacceptable. We have a tradition of success in Anaheim and we need to get back to that."
Carlyle had two stints as Ducks head coach, the first stretching from 2005-12 and highlighted by a championship in 2007. After four-plus years in Toronto, he landed back in Anaheim in 2016-17 and made the playoffs in each of his first two campaigns before the wheels came off this season.
Anaheim currently sits in 28th place with 51 points through 56 games but owns the league's worst goal differential by a wide margin at negative-55. The Ducks also rank dead last in shots per game (27.5) and 29th in shots against per game (34.3) while owning the 29th-ranked power play at 14.9 percent.
Murray has never coached at the NHL level, but he'll guide the Ducks down the stretch until the club begins its search for a full-time replacement in the offseason.