He will be monitored by Palace during his rehabilitation, the club added.
Remy joined Palace on a season-long loan from Chelsea during the transfer window and manager Alan Pardew said the striker had a scan on Tuesday to assess his injury.
"It is obviously a blow for the player and for us as a squad, he has just joined us and we were hoping he would play a big part in the team moving forward," Pardew said.
"He was looking great in training and this was an innocuous injury which can sometimes happen unfortunately."
The 29-year-old French forward has largely found himself on the bench since he joined Chelsea in 2014.
Palace have started the new league season with one point from their opening three games.
(Reporting by Ian Rodricks in Bengaluru; editing by Clare Lovell and Toby Davis)
