The England international was withdrawn with just five minutes on the clock following a clash with Royals striker Adam Le Fondre.
And manager David Moyes has since described the blow as a "bad one" before explaining that the 30-year-old will need to go under the knife.
"I genuinely haven't seen it again but I thought on the pitch it didn't look good," Moyes told Sky Sports News.
"Jagielka knew about it and it is a bad one. He will have surgery tonight to stitch up his ankle. It is a bad one because he is a key player for us."
The Toffees moved within six points of fourth-placed Tottenham with their win ovr Brian McDermott's side.