The incident was not seen by referee Lee Probert nor his assistants at the time. However, after reviewing TV footage, the FA chose to charge Gomes on Tuesday.
It means Gomes will only return for the Toffees’ final game of the season away at Tottenham on May 12.
The Portugal international linked up with the Toffees on a season-long loan in the summer of 2018.
His deal at Goodison Park includes no purchase option, so Everton would have to negotiate a fee in order to secure his services on a permanent basis.
Everton boss Marco Silva has previously admitted that he would like to sign Gomes on a permanent deal after an impressive debut season on Merseyside.
Gomes also revealed last month that he was “really happy” at the Toffees but that no permanent deal had been agreed between the two clubs.
Tom Cairney and Ryan Babel were on target for relegated Fulham on Saturday as the Toffees’ three-game winning run was brought to an end.
That left Silva’s side ninth in the Premier League as they chase a seventh-place finish, which would be enough for a place in the Europa League qualifiers should Manchester City beat Watford in the FA Cup final at Wembley next month.
The Hornets are also in contention for a seventh-place finish. Javi Gracia’s side are level on points with Everton, two points behind Wolves and Leicester.