Rooney was stretchered off the Old Trafford field after the accidental clash with Hugo Rodallega in the home side's 3-2 victory.
United manager Sir Alex Ferguson said: "It was a very bad one. He has gone to hospital. It looks like he will be out for four weeks.
"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.
"Rodallega followed through and caught him - but it was an accident of course."