Mirallas was restored to Everton's starting line-up for Sunday's win over Tottenham after missing the previous four matches due to a hamstring problem.
However, the Belgium international was forced off at half-time and Moyes is now waiting to learn the full extent of the latest complaint.
"We don't think he has done his hamstring, he just felt it had tightened up," said Moyes.
"I don't think it is bad but the last thing you want to see is the recurrence of a hamstring injury.
"You can see what he offered us in the first half, something which we have probably missed."