The 34-year-old Welsh international limped off just before the hour mark as the Hammers could only manage a goalless draw at The Hawthorns.
Bilic sees his side play twice in the next week and is expecting to be without the experienced Collins who to date has made 204 appearances for the east London outfit.
“I don’t know. It was a strange injury, he knocked it in the first half and he continued to play,” he said, as reported by football.london
“Once or twice after that he carried on and after the third one he said to come off, it shows how brave he is.
“Now we will of course scan it but is is an injury, not just a little on but on the other hand, we hope it isn’t too serious.”
Season so far
West Ham’s opening three league matches all took place on the road because of the London Stadium being used for the 2017 World Championships in Athletics.
A humbling 4-0 defeat at Old Trafford to a rampant Manchester United side was followed by a narrow 3-2 defeat at Southampton.
Things got much worse when they left St James’ Park on the wrong end of a 3-0 scoreline at the hands of Newcastle United.
However, returning home, they ran out 2-0 winners against Huddersfield courtesy of goals from Pedro Obiang and Andre Ayew and then followed that up with a goalless draw away at West Brom yesterday afternoon.