The Spaniard accepted the charge of improper conduct, triggering the standard penalty.
Emery apologised to the fan who was struck immediate after the incident and again at the end of the 1-1 stalemate at The Amex Stadium.
Arsenal Manager Unai Emery has been fined £8,000 after he admitted an FA improper conduct charge and accepted the standard penalty. It concerned his conduct during the game against Brighton on 26 December 2018. pic.twitter.com/szlnUmGPIB
— FA Spokesperson (@FAspokesperson) December 31, 2018
"I said to them I'm sorry," the Gunners boss confirmed after the game.
"It wasn't hard but it touched one supporter."
"It's circumstances. I apologised. I hope it's the end of the matter, yes,"
Next up for the Gunners is a clash with Fulham, who visit the Emirates on Tuesday to kickstart 2019.