The on-loan Barcelona midfielder suffered the injury during Saturday's 4-1 win over Fulham.
The 19-year-old has been an impressive performer for Roberto Martinez's men this season, and last week scored a terrific solo goal to earn a point at Arsenal.
Everton confirmed on their official website on Monday, though, that he will now miss "a few weeks" with the injury.
Swansea are Everton's opponents on Sunday, with Sunderland and Southampton making up their Christmas opponents.
They head to Stoke on New Year's Day and then face QPR in the FA Cup.