Bramble missed today's 5-0 defeat at Manchester City after suffering cartilage damage, and Bruce said: "Bramble had an operation a few months ago and he has never felt quite comfortable.
"He had a scan the other day and he could miss the rest of the season.
"We've been told (he needs) complete rest at the moment."
Another knee injury victim, Fraizer Campbell, had been expected to feature in the squad to face City but was also ruled out after suffering a late setback.
Bruce said: "Fraizer Campbell twisted his knee yesterday in training and he will have a scan.
"We are keeping our fingers crossed that it is not a recurrence of the knee injury that he had in August."