Fleury is 35-17-6 with a 2.29 goals-against average and .921 save percentage with five shutouts in 58 games this season.
This is the second time this season Fleury has been sidelined with a concussion, and there is currently no timetable for his return.
The Penguins, who can clinch a playoff spot with a win against New York, will turn to young prospect Matt Murray.
Murray, 21, has done well in the first eight games of his young career, going 5-2-1 with a 2.09 goals-against average and .926 save percentage this season.
He was drafted by Pittsburgh in the third round (83rd overall) of the 2012 NHL Draft.