The Ghana international went off injured in the recent defeat against Manchester City, with Palace forced into an early substitution during the game as a result.
And Palace boss Roy Hodgson has confirmed on Friday that Schlupp will not be available to him for the remainder of the season, with just four games left to play.
It is also uncertain Schlupp, 26, who last featured for Ghana in an international friendly with Mauritania in Accra in March, will regain full fitness in time for a place in Ghana's squad for the 2019 Africa Cup of Nations, which begins on June 21 in Egypt.
"We have been a little bit unlucky in this latter period," he said, speaking at his pre-match press conference ahead of Palace's game against Arsenal on Sunday.
"It started with Mamadou [Sakho], then we lost James [Tomkins] and now we've lost Jeff [Schlupp], which is, of course, three big blows for us.
"He won't play again this season, the ankle injury is such that it will take the three or so weeks we have left [to heal].
"Fortunately, we don't have quite so many other injuries to deal with but we are getting down to our bare bones, but I guess we aren't alone in that respect, late in the season teams do get depleted.
"The worst thing with these things is it always happens to players in the same positions, we are certainly stretched at the moment in our defensive positions, we have been depleted in midfield and up front at the moment, fortunately, we do have competition for places."
Schlupp, who can play in defence or in midfield, has featured 37 times for the Eagles so far this season in all competitions, scoring five goals. Read Full Story