The Dutch striker, who has scored 23 goals so far this season for United, limped out of the 2-0 Premier League win at Loftus Road after colliding with a cameraman in the build-up to Rafael's 24th-minute opener.
Van Persie is expected to miss the weekend clash against Norwich, but should be fit in time for the Champions League last-16 second leg clash with Real Madrid.
United boss Alex Ferguson believes the former Arsenal man should be fine for the clash at Old Trafford.
"Van Persie seems to have collided with the camera dugout. We will assess him tomorrow - it was his hip," Ferguson said afterwards.
"It will be tender but hopefully he will be all right in time for the Real Madrid game."
United drew 1-1 in Madrid.
The victory put United 15 points clear of second-placed City, who face Chelsea on Sunday.