Belgium international Mirallas played 45 minutes in the 2-1 win over Tottenham Hotspur on Sunday after missing the past four matches with a hamstring strain.
However, manager David Moyes said the midfielder needed more time to fully recover from the injury.
"It looks as though we'll lose Kevin for a few weeks and that's a really big blow," he told the club's website.
"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."
Defender Hibbert has made only five appearances this season, having been hampered with a calf injury, and Moyes said he may have surgery next week.
The win over Spurs lifted Everton to fourth spot in the table, although they face a tough challenge against a Stoke side who are unbeaten in six matches.
"It's always a tough place to go because they're a very good team defensively, and physically they're obviously one of the biggest teams in the Premier League so they're a threat from set pieces," midfielder Darron Gibson told Everton TV.
"But we've been on a good run of form the last few games so hopefully if we can keep playing well I think we can go there and get a result."
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