The England international has been charged with breaching Rule E3 by using abusive and/or insulting words towards a match official.
Barry has until 4pm on Thursday to respond to the charge which is believed to relate to an incident after the final whistle of Sunday's match.
If Barry does not contest the charge he will receive a one-match suspension, while any failed attempt to challenge the charge would see the ban increased to two games.
Barry's charge is the latest episode in the fall-out from a controversial encounter which saw United score an added-time winner after their 2-0 lead had been pegged back in the second half.
City have confirmed Matthew Stott, 21, has had his season ticket removed for the rest of the season and faces a lifetime ban if found guilty in court of a charge of pitch encroachment.
In a statement released by his solicitors Stott, a landscape gardener from Knutsford, said: "I would like to apologise to all those affected by my actions, particularly Mr Ferdinand and the other players.
"I am extremely ashamed of my actions. I have let myself down, my family down, my fellow fans down and Manchester City Football Club.
"I intend to write personally to Mr Ferdinand to express my extreme regret and apologies and also apologise to Manchester United and their fans."
Stott is now facing a possible banning order but his solicitor said he had never been in trouble before and was not the "stereotypical drunken football fan".
Police also charged eight other people, including for a racially aggravated public order offence, pitch encroachment, breach of football banning orders and other public offences.
Football Association chairman David Bernstein described the incidents as "deplorable".
"To see Rio Ferdinand with blood on his face is absolutely terrible," he told Sky Sports News.
"I think it's disturbing that we're seeing a recurrence of these types of incidents.
"It's very unacceptable and has to be dealt with severely... in the strongest way we can.
"To my mind it's for the FA, the whole game of football and the authorities to work together to deal with this most severe matter."