The England international stopper picked up the injury during a challenge with Royals' striker Adam Le Fondre in the opening minutes of the Toffees' 3-1 win at Goodison Park on Saturday afternoon.
Jagielka was forced to leave the action immediately and boss David Moyes confirmed that he was going under the knife to repair the damage.
And the Scot, who was not happy about the tackle from Le Fondre, does not know how long the 30-year-old will be missing for but it seems that he is a doubt for next weekend's FA Cup quarter-final clash against Wigan.
Moyes said: "I genuinely haven't seen it again but I thought on the pitch it didn't look good.
"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."