The Togo international had accepted the charge for a malicious stamp on Arsenal's Dutch striker Robin van Persie during City's 4-2 home win last Saturday.
The former Arsenal player, who joined City in July for a fee put at 25 million pounds, will also miss a League Cup home tie against Fulham and a league match at home to West Ham United.
The English Football Association said a separate charge of improper conduct would be considered at a later date. Adebayor's goal celebration in the same match sparked crowd trouble in which a steward was injured.
City said on Wednesday that the club and player had "reluctantly accepted" the violent conduct charge although Adebayor strongly maintained he had not intended to act in such a violent manner.
"He apologised on the day to Robin van Persie personally and to the wider public for the outcome of the challenge," the club added in a statement.
Van Persie had accused his former team mate after the match of setting out to hurt him: "He had his own agenda today and that is bad for football," he added in a statement.
Adebayor was charged with improper conduct after he turned and ran the full length of the pitch to celebrate his goal in front of Arsenal fans who had been shouting abuse at him during the match.
The player has apologised for letting "emotion to take over" and found support this week from Tottenham Hotspur manager Harry Redknapp.
"I've got no time for people kicking anybody or being violent on the football pitch and he was wrong to run the length of the field," he told British newspapers.
"But it's very difficult when you're getting abuse throughout the game like he was. It's not celebrating a goal that causes riots. It's idiots who want to start riots."
