He will now join club captain Robert Koren (broken foot) on the sidelines, while Paul McShane and Maynor Figueroa are also short of full fitness.
"The down side for us is that we've lost another one in James Chester," said Bruce.
"It's a big loss to us and it's one thing we can't afford. Two or three are missing now and we hope that's as much as it gets.
"Ches did his hamstring. He stretched in the last minute trying to make a block but unfortunately his hamstring popped and he'll be out a long time I'd have thought.
"I don't think it's just a grade one tear the way he held it. He's probably out for four to six weeks."