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.
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.
Red Devils' defender Rio Ferdinand was hit with a coin as he celebrated his side's late goal and a fan had to be restrained by City goalkeeper Joe Hart after encroaching onto the pitch.
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