Neto received two yellow cards in the space of three minutes - one for dissent after an Arsenal goal and the second for a foul on Gabriel Martinelli, in the 2-1 loss to the league leaders.
"It was alleged that the player acted in an improper manner by failing to leave the pitch promptly and/or using abusive words towards the match official/s following his dismissal in the 70th minute," the FA said.
It was Chelsea's ninth red card of the season across all competitions and Neto admitted the charge against him. He will miss the match against Newcastle United on Saturday.
The Portuguese winger also faces UEFA disciplinary proceedings after pushing a ball boy during Wednesday's 5-2 Champions League loss at Paris Saint-Germain.