Rangers general manager Glen Sather announced the injury Monday.
"It's a big loss for our team, he was a big part of it," Sather said during a conference call Monday. "Very enthusiastic, upbeat, positive guy and we're sorry to lose him. But we've got some young goaltenders in the organization ... we'll see how things lay out in the future after this."
Goalie Cam Talbot was called up from Connecticut of the AHL to fill the roster spot.
Biron, 33, was 8-6-0 with a 2.13 goals against average in 17 games this season, his first with the Rangers.
Sather is confident Biron can return by the end of the season.
The Rangers are hanging on to the seventh spot in the Eastern Conference. They looked into getting another veteran backup to starting goaltender Henrik Lundqvist before the trade deadline, but found the asking prices to be too high.
"We did look into a [trade] and there were some possibilities," Sather said. "When you're looking for something with short notice like that it gets very expensive to find a backup NHL goaltender that has the experience. We didn't want to just lay a lot of things on the line and I know it's risky, but at the same time, I know that Henrik loves the work and loves to play and he's had lots of time off this year and he's going to have some days between the game that we have coming up. We think he's going to be able to get through this very well."
Information from ESPNNewYork.com's Matt Ehalt The Associated Press was used in this report.