Diafra Sakho went down clutching his knee in the second half of Sunday's 1-1 draw with the Baggies at Upton Park, adding to the Hammers' already injured attacking pair Dimitri Payet and Enner Valencia.
After the match, Bilic admitted it was a worrying time for West Ham who have slipped to eighth on the back of a four-game winless run in the Premier League.
"That worries me more than the result," Bilic said.
"It's still too early before the scan to give a diagnosis but it looks like a muscle injury. It's a big blow for us, he's a key player.
"After losing Valencia and Payet it's a bit too much if I'm honest."