The 21-year-old, signed from Manchester United in the summer in a £9million deal, has made only one start - the Carabao Cup defeat at Bournemouth - in his seven appearances.
He was left behind when the club travelled to Australia for the Sydney Super Cup and manager Frank Lampard has revealed the player is set for an extended absence.
"He's probably going to be back at the back end of January or early February. It's a disappointing injury," he told evertontv.
Fellow midfielder Tom Davies flew back early from Australia after suffering a knee problem in training while injury-prone defender Yerry Mina sustained a hamstring strain in the game against Celtic.
Lampard hopes to have the pair fit again for the Boxing Day resumption of the Premier League campaign.
"Tom is three weeks-ish, which is a positive result as we were worried about him. Yerry is similar, three to four weeks," he added.
Striker Dominic Calvert-Lewin missed Everton's final league match before the World Cup with an ongoing knee problem which saw him sit out the first two months of the season, while winger Andros Townsend is a long-term absentee following anterior cruciate ligament surgery last season.