The centre-back was substituted in the 58th minute the goalless draw at The Hawthorns and is now set for a spell on the sidelines, while there are fears that he may have suffered ligament damage, as reported by the London Evening Standard.
Collins was starting his third Premier League game in succession but West Ham will now have to cope without the services of the 34-year-old.
Impressive at the back, Collins has averaged nine defensive actions per game in the Premier League this season, while he has been successful with 82 per cent of the headed duels that he has contested.
Having taken four points from their five Premier League games so far, West Ham are currently in 17th place in the table. They host Bolton Wanderers tomorrow night in the Carabao Cup third round.