The 26-year-old, who has started all 10 of Albion's league games so far this season, was forced off in the first half of the 2-0 win over Crystal Palace at The Hawthorns last weekend.
He now faces a battle to be fit for the home game against Aston Villa on Monday November 25 when the Baggies return to action following the international break.
West Brom's joint-assistant head coach Keith Downing told the club's official website: "There is a big chunk of time now for him to get it right.
"But we're disappointed because Billy's played well and he's been one of our best players."
Goalkeeper Boaz Myhill sustained a minor Achilles problem against Palace but he is expected to feature against Chelsea.
Downing added: "Boaz had a little bit of stiffness in his Achilles. That was scanned and it is clear.
"He should be fine for the weekend. There are no alarms or worries about that. He was just limping a little bit and had a bit of soreness."
Strikers Victor Anichebe and Nicolas Anelka are also expected to be available for selection after missing the visit of the Eagles due to a tight hamstring and illness respectively.
"Nico trained on Sunday, so he's back and well," said Downing. "Victor is in and around it again; he had tightness and it was more precautionary than anything else."
Winger Scott Sinclair has been out for almost six weeks due to a hamstring injury but is now back in training and a decision on whether or not he is fit to face his former club will be made later in the week.