The Dutchman crashed into a television camera, situated just beyond the by-line, in the build-up to United's first goal. Encouragingly, he played on for 18 minutes following initial pitchside treatment, but eventually departed just before half-time, replaced by Danny Welbeck.
Sir Alex told MUTV after the game: "He collided with a camera, which was in a dug-out piece of ground. He hit the base of it and has a very bruised hip."
He added on Sky Sports: "I imagine it will be tender and sore for a few days but hopefully he will be all right, especially for the Madrid game [on Tuesday 5 March]."
Van Persie joined his team-mates on the bench at Loftus Road to watch the second half, as United turned the screw and, with 10 minutes to play, added a second goal to secure three valuable points.
The Reds' next test comes against Norwich City on Saturday 2 March, followed by the second leg of the Champions League last 16 tie against Real Madrid on Tuesday 5 March.