Mara had a brief examination of his shoulder at Madison Square Garden, but swelling prevented a closer look. He was immediately ruled out of Monday's road game against the Blues and left the arena with his right arm in a sling.
The fight was stopped when Mara was injured 6:14 into the third period of Philadelphia's 5-2 victory.
"The first two punches I was swinging and I could feel something in there and I stopped," Mara said. "Give Arron a lot of credit. The respectful player that he is, he stopped. It was a very good character thing on his part."
Mara, who conveyed that sentiment in a conversation with Asham, said he has never had a shoulder injury and held out hope he could return quickly from this one.
The 6-foot-4 Mara has been one of the Rangers' most consistent defensemen this season and has played with an added measure of snarl throughout his 56 games.
"We'll take it day by day and see how it feels in the next couple of days," the 29-year-old veteran of 10 NHL seasons said.
"Right now it's pretty painful so they'll wait a couple of days, wait for the swelling to go down and assess it."
Mara has five goals and 11 assists this season with a minus-2 rating. He had been a plus until Sunday, when he was on the ice for three Flyers goals.
The Rangers have a history of shoulder injuries during fights. Former captain Jaromir Jagr hurt his right shoulder in a 2006 playoff loss at New Jersey when he threw a punch at Devils forward Scott Gomez, who is now in his second season with the Rangers.
Jagr eventually required surgery and needed until well into the 2006-07 season before he was back to full strength.