Murray, the Championship's top scorer this season with 30 goals, was carried off on a stretcher with a knee injury during the first leg of Palace's play-off semi-final against his old club Brighton last Friday.
Eagles chairman Steve Parish confirmed the 29-year-old has torn his cruciate ligament and will have an operation in the next couple of weeks.
"It's a pretty bad one," added Parish.
Murray attended the second leg at the Amex Stadium on Monday night on crutches as two goals from Wilfried Zaha fired Palace to Wembley.
When he recovers from his injury Murray could be a Premier League player - the Eagles will now take on Watford for a place in the top flight on May 27.