The forward was injured in a 5-3 win against the Carolina Hurricanes on Friday.
Lemieux, who was acquired Feb. 25 in a trade with the Winnipeg Jets for forward Kevin Hayes, had 13 points (five goals, eight assists) in 35 games this season and led the Rangers in penalty minutes (87).
The Rangers recalled forward Steven Fogarty from Hartford of the American Hockey League and he played 2:46 in a 5-4 overtime win against the Toronto Maple Leafs.