Gomes, on loan from Barcelona, faces a potential three-match ban for an alleged stamp on Fulham striker Aleksandar Mitrovic at Craven Cottage.
The incident in the 95th minute of the match was missed by referee Lee Probert, but was caught by the FA after a review of video evidence.
Gomes, 25, has until 6 p.m. local time on Tuesday to respond to the charge.
If the suspension takes effect, the Portugal international would miss the ninth-placed Toffees' Premier League clash with Manchester United on Sunday, as well as games against Crystal Palace and Burnley.
Information from Reuters was used in this report.