The Gunners boss was fuming after his side conceded a dramatic equaliser in the fifth minute of stoppage time at the Stadium of Light, which denied them the chance to go top of the Premier League table.
Wenger appeared to sarcastically pat Martin Atkinson on the back as Darren Bent's goal came 15 seconds after the allotted four minutes, and was also critical in his post-match comments.
The Arsenal manager could accept the charge and a one-match touchline ban and £8,000 fine under the FA's new fast-track disciplinary procedures.
A statement on the FA's website read: "Arsenal manager Arsene Wenger has been charged with using insulting and/or abusive language and behaviour amounting to improper conduct.
"The charges relate to Wenger's conduct towards match officials at the conclusion of Arsenal's match against Sunderland on September 18.
"Under the FA's new fast-track procedures, Wenger has until Thursday, September 23 to respond to the charge and he has been offered a standard sanction of a one-match touchline ban and an £8,000 fine should he accept the charge.
"If he denies the charge, the case will be heard by a Regulatory Commission."
Wenger could not see why any additional time should have been played. Speaking after the match, refereed by Phil Dowd who sent of Gunners midfielder Alex Song for two yellow cards, the Arsenal manager lamented: "It was outside the four minutes.
"I know the referee can give more than four, it's a minimum of four minutes, but in the four minutes nothing happened to justify the extension of the time.
"But I cannot do anything about that.
Wenger added: "If you have a watch, you can control. It's as simple as that."
Asked about a suggestion he had put his hands on Atkinson, Wenger replied: "Take the pictures and look at it.
"I complain to nobody, especially not to you."
Last season, Wenger received an apology from referees chief Keith Hackett over his dismissal during the Gunners' 2-1 loss to Manchester United during August 2009.
Wenger was sent to the stands by referee Mike Dean in the dying moments at Old Trafford on the advise of fourth official Lee Probert after the Arsenal manager kicked a water bottle following a disallowed goal which would have been a last-minute equaliser.
After his sending off, Wenger was unaware of where to go and firstly moved to the Arsenal dugout, then the main stand before being ushered along the touchline to the tunnel.