The 25-year-old suffered the problem during the Tigers' 1-0 defeat to Norwich City last weekend after just 15 minutes.
"James has damaged the tendon again, the one that he damaged at the start of the season," Goal.com quotes Bruce as saying.
"It's not as bad as it was the first time he did it, but it's still a concern because it is the same tendon high up in his hamstring. He's going to be at least six weeks away I would have thought. It's a shame because he was just finding his feet again after his last spell out, but that is football."
Hull are currently 11th in the Premier League table.