The Spanish coach immediately apologized to the supporter following the incident during the closing moments of Arsenal's 1-1 Premier League draw at the Amex Stadium last Wednesday.
Emery admitted an FA improper conduct charge and accepted the standard penalty.
"I kicked it for me and it went near the supporters. I said my apologies ... I kicked it because it's near me and not because of this intention," Emery had said following the incident.
Arsenal, who are fifth in the table following a 5-1 defeat by leaders Liverpool on Saturday, host Fulham on Tuesday.