The Toffees also revealed that a formal complaint has been registered with Merseyside Police, who are themselves investigating the matter and may take further action.
The fan in question attempted to strike Lyon's Anthony Lopes during the second half of the French side's 2-1 win, with matters boiling over after Everton skipper Ashley Williams barged into the visiting goalkeeper.
A number of players were caught up in the melee, which ultimately ended with just a couple of yellow cards being dished out by Dutch referee Bas Nijhuis.
An Everton statement read: "Club officials have reviewed the footage of an incident that occurred in the 64th minute of the game against Olympique Lyonnais where supporters towards the front of the lower Gwladys Street End became involved in a confrontation between players.
"We have identified one individual whom action will now be taken against. This will include a ban from attending future Everton fixtures and the club registering a formal complaint with Merseyside Police."
Lopes has attempted to play down the incident, which UEFA is expected to investigate at a later date.