Rooney was replaced by Robin van Persie in the dying minutes of the match, which United lost 3-0.
As of right now, United manager Louis van Gaal is unsure how serious Rooney's injury is and how long he will be out for as well.
"Yes, Rooney was injured," he said during the post-match press conference. "He had a shot on his knee, so we have to wait and see how heavy [serious] it is."
Meanwhile, van Gaal also pointed out that he had to remove midfielder and former Everton player Marouane Fellaini at half-time since the 27-year-old was shown a yellow card in the 12th minute.
"He was booked and I found that the players of Everton provoked him and I was not so sure if he should end the match," he said. "That is a reason, but also because of the result at half-time and of course I could have changed more players."