Mirallas To Miss Stoke Clash
Tony Hibbert also ruled out for Blues.
Belgian Mirallas had been sidelined with a hamstring strain since November's victory over Sunderland, but returned to play the first 45 minutes against Tottenham last weekend.
Moyes withdrew the forward as a precaution, but admitted on Friday that he will now be given more time to reach full fitness.
The Blues boss said: “It looks as though we'll lose Kevin for a few weeks and that’s a really big blow. Anyone who has watched our games will tell you what he is like.
“His hamstring just isn’t right so it looks like we are going to have to take more time over it. It will probably keep him out for a while.
“We originally thought it would be a mild hamstring injury and we gave it extra time and I was actually expecting him to be available for the midweek Arsenal game.
“I didn’t then use him in the Manchester City game in the hope that he would be right for the Tottenham.
“We gave it extra days to get him right but we will now need to take even more time, unfortunately.
“He will be a big miss for us because he gives us a different attacking dimension from what we have got.”
Meanwhile, full-back Hibbert has been similarly in and out of the Blues' set-up this term through injury.
Despite returning to the Everton side for the 1-1 draws with Arsenal and Manchester City, a calf problem has since resurfaced and will now be treated on Monday.
Moyes said: “Tony has got a reccurrence of his calf injury so we think he is going to have an operation at the start of next week which will keep him out for a while as well.
“We've got a few niggles and knocks like everybody else, the odd one or two here, but I think it's going to be like that around this time of year. You can pick up an injury in training nowadays and the players are right in the middle of the cold weather in training.”