The 31-year-old "reluctantly" accepted the punishment after the charge arose from an incident after City's derby defeat to Manchester United on Sunday.
"Manchester City's Gareth Barry will serve a one-match suspension with immediate effect after admitting a breach of FA Rule E3 in that he used abusive and/or insulting words towards a match official following his side's match against Manchester United on Sunday 9 December 2012," said the FA's statement.
"Also as part of the standard penalty for this offence, Barry has been fined £8,000."
In posting the statement on their website City said "both the club and Gareth Barry reluctantly accept the punishment which leads to Gareth being unavailable to take part in the weekend's match against Newcastle."
Barry will be available for selection again for the home game against Reading on December 22.