Despite initially playing on the 24-year-old hobbled off soon after having received medical attention.
Emerson Palmieri replaced Chilwell, who has impressed for the Blues since his £45million switch from Leicester.
The news will come as a major concern to manager Frank Lampard as he approaches a hectic festive schedule with Reece James already sidelined through a knee injury.
The Blues took the lead shortly after thanks to a powerful header from veteran centre-half Thiago Silva, the former Paris Saint-Germain defender’s second goal for Chelsea since joining the club on a free transfer.
Lampard’s men rode the storm after the interval with the visitors dominating possession, before Tammy Abraham doubled Chelsea’s lead with 12 minutes remaining.
Werner cut inside and saw his weak shot tapped in by Abraham, who was played onside by Aaron Cresswell.
Two minutes later the Blues put the game out of West Ham’s reach when the England international fired home to make it 3-0 after Lukasz Fabianski had kept out Christian Pulisic’s header.
Speaking after the match, Lampard revealed that Chilwell will have a scan on Tuesday to determine the extent of the problem.
He said: “I expect he’s doubtful for Arsenal. He turned his ankle and it was too painful to continue.
“We’ll have a scan tomorrow to see how bad the injury is and update after that.”