The England midfielder will miss the Premier League game at Selhurst Park after aggravating an existing foot problem during Wednesday's 3-2 League Cup quarter-final loss to the Gunners at the Emirates.
The 26-year-old first suffered the injury during last weekend's 3-1 Premier League win at Brighton but played on against Arsenal.
"We have no-one back yet, but we do have one more injury: Ebs is unavailable," Palace manager Oliver Glasner told a pre-match press conference on Friday.
"He got a hit against Brighton on his foot. He played with quite a swollen foot at the Emirates and also got the next kick there, so he is not 100 percent.
"We need every player 100 percent, so it makes sense. We decided that he gets a rest and hopefully he will be available for Bournemouth."
Glasner added: "It doesn't look serious, but you have to wear the boots, kick the ball and it is painful. It is not that free in terms of movement.
"You always feel pain when you move and then you are thinking too much about this and can't play how you can play.
"We need the best Eberechi Eze he can be and therefore he has to be fit like all the other players."
The Eagles will now try to extend their unbeaten league run to six games without Eze as they head into the traditionally busy Christmas and New Year programme.
Victories over Ipswich and Brighton, allied to draws with Aston Villa, Newcastle and Manchester City, have taken Palace into 15th place -- four points clear of the relegation zone.
"For me the busiest part of Christmas is this week, three games in six days," said Glasner. "We have one game on the 29th, but then we have a week until Chelsea, so the busiest period is now and it is good to have players available.
"And I expect Ebere to be available for Bournemouth. Of course it is important to have your team together, and we will go for getting a better result than two days ago at the Emirates."
