The striker was brought on as a second-half substitute as Sir Alex Ferguson's side secured a 3-2 win but was withdrawn in the closing stages with a nasty-looking cut
Coming off the substitutes bench with just over 20 minutes remaining, a clash with Hugo Rodallega in injury time forced the England international to be stretchered from the pitch.
Sir Alex Ferguson confirmed after the game that Rooney has since been sent to hospital and could face a month in rehabilitation.
"It's a very bad gash. He's been sent to hospital and I think he'll be out for four weeks," Sir Alex told Sky Sports.
"Rodellaga followed through after his shot. Obviously it was an accident."
Focusing on the game itself, Fulham took the lead after just three minutes when Damien Duff latched onto Bryan Ruiz's free kick.
United responded strongly with three first-half goals from Robin van Persie, Shinji Kagawa and Rafael - the former two with their first for the club.
A mix-up in between David de Gea and the defense led to Nemanja Vidic knocking the ball into his own net with 25 minutes still on the clock, but the west London outfit could not find the all-important equalizer.