The 29-year-old, who has a history of knee problems, suffered the injury when denying David Ngog a shooting opportunity during the 2-1 setback at Goodison Park.
Toffees manager David Moyes confirmed on Friday that the England international would be "probably out for up to six weeks" with medial ligament damage.
"Jags has got medial ligament damage," said Moyes. "Losing Jagielka is an incredibly big thing for us because the one thing about the team at the moment is they have been very strong defensively in the main.
"Whether it has been Jagielka with Sylvain Distin or John Heitinga that has worked really well for us.
"To lose him is a massive blow to us because he is an integral part of the defence and very important to us."
Injuries are starting to add up for Everton as Moyes also revealed midfielder Leon Osman, one of his better players in recent weeks, also has a problem which could sideline him.
"Leon Osman has a floating bone in his knee which we think will have to be taken out and we have a few other injuries kicking around as well - Tim Cahill, Ross Barkley (knee) and Jack Rodwell (hamstring).
"Jack's had a recurrence of his hamstring injury. It is not serious but every time we get him scanned it is a grade one and very light and he comes back and doesn't feel anything.
"We maybe just need to give him a week or so longer to make sure he is right this time."
