Quinn's is the third prominent firing by the Rangers in the past week. They fired president John Davidson and general manager Jeff Gorton on May 5, when Chris Drury was named New York president and GM.
Assistants David Oliver, Greg Brown and Jacques Martin were also fired Wednesday. Goaltending coach Benoit Allaire was retained.
Drury said the search for a new coach has begun.
Quinn finished his third season with the Rangers on Saturday with a 5-4 win against the Boston Bruins at TD Garden. He was 96-87-25 (.522 points percentage).
"There's so much that's gone on and that might get lost in all of this," Quinn said after the game. "It's a great opportunity for [Drury]. I know all of us and our players were very happy that we were able to get him his first win as a general manager."
New York (27-23-6) is fifth in the eight-team MassMutual East Division, failing to make the Stanley Cup Playoffs. The top four teams in the division qualified.
The Rangers were part of the NHL Return to Play Plan last season and were swept in three games by the Carolina Hurricanes in the best-of-5 Stanley Cup Qualifiers. They did not make the playoffs in 2018-19, Quinn's first season.
Quinn was hired May 23, 2018, after five seasons as the coach at Boston University, his alma mater.
He is the third NHL coach removed since his team's regular season ended. It was announced Sunday that John Tortorella would not return to the Columbus Blue Jackets and that Rick Tocchet would not be back with the Arizona Coyotes.
