The midfielder has sustained ankle ligament damage and is unlikely to play again in 2015/16 while winger Jason Puncheon has suffered a hamstring injury and is set to be out for a few weeks.
Eagles boss Alan Pardew said: "We've had some disappointing news: McArthur's out for a long period we think.
"And Puncheon's going to miss a long period as well. It's a hamstring (Puncheon) for one and the other is ankle ligaments (McArthur), so that's a couple more injuries to the list."
It is further bad news for Palace who have lost their five matches to slip to 12th on the Premier League table.