Chilwell, who was substituted after 10 minutes following a collision with West Ham forward Jarrod Bowen,
could also miss Saturday's Premier League game against Arsenal.
"I expect he'll be doubtful for Arsenal. He turned his ankle and tried to carry on but it was too painful," manager Frank Lampard said after the game.
"We'll have a scan to try and see how bad the injury is. We'll update after."
Reece James was also ruled out of the game against West Ham due to a knee injury but Lampard said he hoped to have both his full backs fit ahead of a packed festive schedule.
"Reece and Chilly have been doing really well, we hope their injuries are not that bad and they will be in and around the games over Christmas," Lampard added.
基本上即係Chilwell出唔到對阿仙奴, R.James就未知掂