Rooney, who surprisingly started on the bench rather than partnering new signing Robin van Persie up front, had blood streaming from his leg after being caught by the boot of Hugo Rodallega and had to be carried off on a stretcher.
"He's got a very bad gash. It looks as if he'll be out for about four weeks. Obviously you've got to be careful with these things because of infections," Ferguson told Sky.
England forward Rooney, now doubtful for the first Champions League group game in mid-September, had started Monday's opening 1-0 defeat at former club Everton when former Arsenal striker Van Persie was on the bench.
United were cavalier at times at Old Trafford, going 1-0 down early on after a lack of awareness at a free-kick allowed Fulham's Irish winger Damien Duff - who announced his international retirement in the week - to slot home.
Van Persie with a trademark volley on his first start, Japan's Shinji Kagawa with a tap in on his home debut and a rare Rafael header helped United storm back into the lead but a strange own goal from Nemanja Vidic gave Fulham late hope.
"We were playing absolutely great football. Then we lose a stupid goal, bad defending and it made a game," Ferguson added, aware that poor play at the back towards the end of last season contributed to United losing their title to Manchester City.
Ferguson, though, could only praise former Arsenal striker Van Persie for the Dutchman's effortless 10th-minute strike.
"It was a fantastic finish, absolutely brilliant, it epitomised the type of goal-scoring ability he has. It lifted the place," he said.
