The 26-year-old, who joined the Tigers from Norwich City earlier this summer, was withdrawn shortly before half time at Loftus Road following a coming together with Joey Barton.
"Snodgrass is a concern," Bruce is quoted as saying by FourFourTwo. "He's twisted his knee. He's in a brace and crutches at the moment.
"Touch wood he's not too bad, but we fear ligament damage. If it is, of course, it means it's going to be a long time, so let's hope it's not."
Alex Bruce was also replaced at half time, but Bruce stated that the injury was only minor.