Maurice, 46, has coached the Caroline Hurricanes and the Toronto Maple Leafs with an NHL record of 460-457-167.
Under Noel's guidance, the Jets had lost five games in a row, dropping them a full 10 points behind the last playoff spot in the Western Conference.
The team also axed assistant coach Perry Pearn but did not immediately announce who would replace him.
Noel was hired in the 2011-12 season after the Atlanta Thrashers were relocated to Winnipeg. He went 80-79-18.
An early message of support for Noel came from former Blue Bombers coach Paul LaPolice. LaPolice was fired from his post after a string of losses in August 2012.
On Sunday, he tweeted, "Sorry to hear about the Jets firing Claude Noel. Good man and it's not always the coaches fault."
Winnipeg Jets general manager Kevin Cheveldayoff was expected to speak about the change at 1:30 p.m. on Sunday.