Morrissey was injured in the third period of a 4-1 loss at the Arizona Coyotes on Sunday on a hit from forward Vinnie Hinostroza.
"Josh will be out through the month of March and his window will open sometime in early April," Maurice said after Winnipeg's pre-game skate.
The Jets (37-21-4), who have lost four of their past five games, host the Minnesota Wild on Tuesday (8 p.m. ET, TSN3, FS-N, FS-WI, NHL.TV). Winnipeg is in second place in the Central Division, one point behind the Nashville Predators and six points ahead of the St. Louis Blues.
Morrissey, who has missed three games this season because of different lower-body injuries, has 31 points (six goals, 25 assists) in 59 games and ranks fourth on the team with an average of 22:24 of ice time per game.
Nathan Beaulieu, who the Jets acquired for a sixth-round pick in the 2019 NHL Draft on Monday, will replace Morrissey on the top defensive pair alongside Jacob Trouba.
