The Hungary captain suffered the setback after 21 minutes at The Hawthorns. He will undergo further scans this week but Baggies boss Roy Hodgson fears the worst.
He told the club's official website: "Zoltan has done really well since coming into the team three games ago and his performances quickly justified how highly we rate him.
"We still don't know for sure how long he will be out for but we know we won't be able to call on his services for the foreseeable future. This will be a major blow both on the training pitch and the match arena.
"Zoltan is now in the hands of our excellent medical and sports science department and we just have to hope and pray that his stint on the sidelines is not an overly prolonged one."