A source confirmed to ESPN's Adam Schefter that Clay had a torn meniscus and MCL sprain. The news about Clay's diagnosis was first reported by Pro Football Talk.
McDermott said Monday he had yet to speak to doctors about the injury and was not sure whether it would be season-ending.
"Next man up, that's what we do," McDermott said. "That's what happens in the league. Sometimes this happens. We've gotten hit a little bit by the injury bug."
Clay leads the Bills this season with 258 yards on 20 catches. He is also tied for the team lead with two touchdown receptions.
Clay was hit in his left leg by Bengals safety Shawn Williams after a 24-yard catch during the first quarter Sunday. He remained on the ground in apparent pain before being walked to a medical tent on the sideline with assistance from two members of the Bills' training staff. Clay later walked gingerly to an awaiting cart.