Callahan, who scored the winning goal in the 2-1 victory, was injured early in the third period during a scuffle with Philadelphia forward Max Talbot.
After undergoing an MRI on Wednesday, the Rangers said Callahan was diagnosed with a subluxation of his left shoulder. Callahan was dragged down by the arm by Talbot and immediately skated off the ice. His left arm dangled as Callahan went down the tunnel to the locker room.
If the timetable is correct, Callahan would miss six games over the next two weeks —beginning with visit by Atlantic Division rival Pittsburgh on Thursday night.
Callahan is one of the Rangers' best penalty-killers and defensive forwards, and those are the areas in which he'll be missed most. The Flyers' lone goal Tuesday night came on a power play not long after Callahan left the game.
"I don't think you fill his role," Rangers coach John Tortorella said Wednesday. "I felt that in the third period [Tuesday] night when we were protecting the lead, that's a very big part of his game.
"Every team goes through the injuries, and just playing that much better in the situations that he's been put in through his career, it needs to be done as a group. You lose a top guy like that, it shuffles the lineup, and it gives other guys chances that they probably wouldn't get if he was playing. I feel comfortable in us joining together as a team and trying to get it solved until we get him back."
The Rangers have won back-to-back games after dropping three of their first four.