Rooney was carried off the Old Trafford field on a stretcher after the accidental clash with Hugo Rodallega in the home side's 3-2 victory. The England striker is expected to be out of action for four weeks.
Rooney was charging down a shot by the Fulham substitute, whose boot connected with the England striker's leg.
Television pictures showed a severe gash down Rooney's right leg, with blood coming from the deep wound.
United manager Sir
If Ferguson's assessment proves correct it would rule Rooney out of England's EURO 2012 double-header with Moldova and Ukraine at the beginning of next month.
In addition, the 26-year-old would miss the start of United's UEFA Champions League campaign, whilst also making him a major doubt for the Red Devils' crucial trip to Liverpool on 23 September.
"You have to be wary of infection and that kind of thing so he has gone to the best place and hopefully he will be okay," added Ferguson.
"Rodallega followed through and caught him - but it was an accident of course."
Rooney's injury capped a bad day for the striker, who had been dropped by Ferguson, who handed Robin van Persie his first start.
That Van Persie levelled Damien Duff's early opener and impressive strike partner Shinji Kagawa also got his name on the scoresheet made it doubtful Rooney would have started at Southampton next weekend anyway even without his enforced lay-off.
Certainly Ferguson was happy at the way Van Persie and Kagawa combined in a thrilling first-half display.
"It was fine," he said.
"Obviously it is early doors and there will be a better understanding as time goes on."
And it seems Ferguson is intent on operating with someone occupying a deeper role behind Van Persie, suggesting Rooney will not be able to take his first-team place for granted.
"We normally do that, whether it is Wayne who plays in that role, or Danny Welbeck can do it," said Ferguson.
"Ashley Young and Ryan Giggs can play there. We have options that way."
That United should be so imperious before the break but end up clinging on just added to a strange day that included the presentations of Olympic superstar Usain Bolt, in addition to long-jump goal medalist Greg Rutherford on the pitch.
Bolt had not even take his seat when Duff put the visitor in front.
However, United responded by creating a succession of opportunities and it was well worth the half-time advantage provided by Van Persie, Kagawa and Rafael, who headed home just before the interval.
After the break though United's defensive frailties came back to haunt it, with David de Gea getting in a real mess trying to clear a routine cross, which ended with Nemanja Vidic putting the ball into his own net.
"The first-half performance was fantastic," said Ferguson.
"It could have been five, six, anything.
"But we made a terrible mistake for the second goal and it becomes a match. Before that it had never been a match."
Ferguson confirmed Jonny Evans would have been available off the bench in an emergency, although in the end the Northern Irishman was not needed and should be available for the trip to Southampton.
Fulham manager Martin Jol admitted he was surprised at Rooney's absence from United's starting line-up.
"I was surprised," he said. "I thought Van Persie and Rooney would play.
"I know Kagawa from my time in Germany and I knew he would not play on the left. I thought it might have been an advantage because my players did not know him.
"He is a quality player. But Rooney is a fantastic player as well."
Meanwhile, Jol expressed concern at the plight of Clint Dempsey, who was again missing after spending the last five weeks training with the Fulham physios as he hankers after a move to Liverpool.
"Everyone thinks he was left out of the squad today but he has not been there for four or five weeks," said the Fulham chief.
"If there is no bid - like Steven Fletcher and Matt Jarvis at Wolves - he could have played until he got his big move. I would have liked that.
"But there is no official bid. It is a very bad situation for us, and for him of course."
And Jol wonders if something will happen before the transfer window closes on Friday to save him dealing with a very difficult situation.
"I am not a person who will not forgive a player," he said.
"I loved him last year but I have not seen him much this year.
"If there is no bid what can I do? I cannot sell him to the non-league or put him on loan at Stevenage.
"Maybe something will happen next week.
"He really thought he would be on the move four or five weeks ago. His head was turned.
"He thought it would happen in the next couple of days and it didn't."
English Premier League