The England striker was carried off on a stretcher in injury time after Hugo Rodallega landed on the forward’s leg as Rooney attempted to block a shot.
“Wayne Rooney’s been whisked off to hospital immediately and it looks a bad one,” Ferguson told BBC Sport. “I think he could be out for four weeks with a bad gash.”
Rooney was a second-half substitute for Manchester United new-boy Shinji Kagawa, who marked his home debut with the second goal in the win over the Cottagers 10 minutes before half-time.
Robin van Persie’s first United goal had hauled the Red Devils back level after Damien Duff put the visitors ahead within three minutes.
And Rafael made it 3-1 to Ferguson’s men before the break after Kagawa’s strike. A Nemanja Vidic own goal in the 64th minute set up a tense finale but the home side held on to claim their first win of the new season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news