The England international accepted the charge of the suspension as well as an £8,000 fine meaning he will miss his side's clash with Newcastle on Saturday.
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Barry accepted the punishment for using abusive language towards fourth official Mark Clattenburg in the tunnel minutes after his side's 3-2 defeat to United.
The news of the 31-year-old's suspension will come as a bitter blow for City boss Roberto Mancini, as Barry has been a key player for his side this season featuring in 17 games so far in all competitions, after returning from a hernia operation in September which kept him out of Roy Hodgson's England squad for Euro 2012.
A statment on the club's official website 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."
It is expected Barry will return to first-team action next week for City's Premier League clash with Reading.