Scholes was shown a striaght red card for deliberate handball on the goal-line which led to Fulham scoring their first goal from the resulting penalty.
Rooney was shown a second yellow card for allegedly throwing the ball in the direction of referee Phil Dowd in the final minute of the 2-0 defeat at Craven Cottage on Saturday afternoon.
Both players will now have to serve an automatic one game suspension and will miss United's next Premier League match against Aston Villa at Old Trafford on Sunday, 5th April.