City said they 'reluctantly accepted' the charge against Adebayor for his stamp on former team-mate Robin van Persie in last Saturday's Premier League 4-2 victory over the Gunners.
That will cost 25-million-pound signing Adebayor a three match ban - if found guilty following Thursday's hearing - starting with this weekend's derby.
City will contest the second charge of improper conduct for the player's goal celebration in front of the Arsenal supporters, which saw him run the length of the pitch to taunt them. City have until September 30 to respond to that charge.
After the match it emerged that a steward needed hospital treatment after being hit by an object thrown from the crowd following Adebayor's celebratory actions.
Following the announcement about not contesting the first charge, City's statement added: "Adebayor strongly maintains that he did not intend to act in a violent manner.
"He apologised on the day to Robin van Persie personally and to the wider public for the outcome of the challenge."
Adebayor, who signed for Arsenal from French First Division side Monaco and was generally a hit at the club, said emotions "took over me" and it was "silly" to run up to the fans, but revealed that he had been insulted for the whole game.
Premier League chief executive Richard Scudamore said on Monday that these instances "don't do the image of the league or football in general any good".
Providing the FA confirms a three-match ban on Thursday, as well as missing Sunday's match with United, Adebayor will also sit out the League Cup tie with Fulham next Wednesday and a Premier League meeting with West Ham.
With Adebayor likely to miss the match, City will have only one striker available for the United match in volatile Welsh international Craig Bellamy.
Brazilian Robinho, Paraguayan Roque Santa Cruz and Zimbabwean Benjani Mwaruwari are all injured, while former United hitman Carlos Tevez is rated extremely doubtful after suffering an injury duriong Argentina's World Cup qualifier defeat to Brazil 10 days ago.