Quinn twisted his knee during training on Thursday and missed Saturday's win at Huddersfield.
"He jarred his knee and was uncomfortable over the weekend," Bruce said. "He had scans on Friday and there's nothing too serious.
"Hopefully he might be available for Tuesday."
Meanwhile, Bruce reaffirmed that a two-year contract has already been agreed with matchwinner George Boyd, who scored his fourth goal in six appearances for the Tigers since arriving from Peterborough in an initial loan deal last month.
"The deal's done," Bruce added. "Even if we're not promoted."