Neto was shown a red card after two bookings in quick succession after he was accused of exiting the pitch in an "improper manner" and using "abusive words" towards the match officials.
A statement from a spokesperson of the FA said: "Pedro Neto has been given a one-match suspension and a £70,000 fine for misconduct that occurred after he was sent off in Chelsea's Premier League match against Arsenal on Sunday 1 March.
"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.
"Pedro Neto subsequently admitted the charge against him. An independent Regulatory Commission imposed these sanctions following a hearing, and the written reasons for its decisions will be published in due course."
Chelsea, who have seen nine different players receive red cards this season have shown a lack of discipline this season which has become a problem for Liam Rosenior who has tried to control his squad’s behaviour behind closed doors.
Neto could face a further ban?
Neto also pushed the ball boy in frustration, trying to get the ball back against Paris Saint-Germain in midweek as UEFA investigate the incident that could lead to a further ban.
Rosenior said: "I've seen the incident back now, it doesn't look good in terms of... I understand Pedro's perspective. He wants to get the ball back in play as quickly as possible, he wants to win for the club. There are ways you go about it.
"What I was so impressed with him was, and it was his idea, he wanted to apologise straight away. Like I've just said, whether it's a goalkeeper, whether it's me as the manager or a player, we make mistakes. It's about learning from those mistakes and making sure they don't happen again."