One person has been charged with a racially aggravated public order offence, and two with pitch encroachment. Two other men were charged with breaching a football banning order, one a section 5 public order offence and three with being drunk and disorderly.
All nine men are due to appear before Manchester City Magistrates' Court on January 4, while four other arrests were made.
However, Greater Manchester Police are still attempting to identify the person involved in an incident that saw Manchester United defender Rio Ferdinand struck by a missile.
Chief Inspector Steve Howard said: "To have just 13 arrests for a crowd of this size and a match of this proportion is a testament to the policing operation we put in place.
"Despite fierce rivalry and high tension there was no major disorder. However, we will continue to investigate the coin throwing incident and are determined to work with the club to bring the perpetrator to justice."
Ferdinand suffered a cut above his eye when celebrating Robin van Persie's late winner in a 3-2 victory for United at the Etihad Stadium, and was also confronted by a City fan, before Joe Hart intervened.
The fan, 21-year-old Matthew Stott, has now apologised to Ferdinand in a statement through his solicitors.
He said: "I would like to apologise to all those affected by my actions yesterday, particularly Mr Ferdinand and the other players. I am extremely ashamed of my actions. I have let myself down, my family down, my fellow fans down and Manchester City Football Club.
"I intend to write personally to Mr Ferdinand to express my extreme regret and apologies and also apologise to Manchester United and their fans. I would like to thank Joe Hart for his actions when I came on the pitch.
"I have been a fan of Manchester City Football club all my life and I have been a season ticket holder for three years and I attend the games with my father. I have had the same seat in the section next to the away fans for those three years."
Rebecca Caulfield, solicitor at Stephen Lickrish & Associates, said to the Manchester Evening News: "Mr Stott is a hard working man who has held a full time job as a landscape gardener for four years and lives with his partner of five years. He has never been to court before and has never been in trouble with any of the stewards at Manchester City Football Club before or at any other ground. He is extremely remorseful and is mortified by his behaviour which is completely out of character.
"This was a momentary mistake by Mr Stott which has led to him being charged, brought shame on his family, and will bring sanctions on the club that Mr Stott has supported all his life.
"Mr Stott will accept the consequences of his actions. He would like to make clear that he is not the stereotypical drunken football fan but a fan that attends games with his father. He is embarrassed and ashamed of his temporary moment of madness that has brought wider consequences on the club he supports and his fellow fans."
City apologised for the incident on Sunday, and confirmed that Stott has had his season ticket removed for the rest of the season and faces a lifetime ban if found guilty in court of a charge of pitch encroachment.
"His season card has been immediately removed for the rest of the season and he has been charged to appear at court. If he is found guilty he faces a lifetime ban," said a City spokesman.
FA chairman David Bernstein has called the crowd incidents at the Manchester derby "deplorable", and says they must be "dealt with severely".
Bernstein told Sky Sports News: "It is deplorable to see those incidents, and to see Rio Ferdinand with blood on his face is absolutely terrible."
He continued: "I think it's disturbing that we're seeing a recurrence of these types of incidents. We've had racial abuse issues, the odd pitch incursion, things being thrown at players - it's very unacceptable and has to be dealt with severely."
Bernstein promised tough action from the FA to try to stamp out the chances of further incidents occurring.
"It's very disappointing: so much of football is so good, great things are happening in football as a whole, but these odd incidents get the headlines - and understandably because they are serious matters, they are unforgivable things," he added.
"When you think of the millions watching football every week, or involved in football, to see it hijacked by these incidents is awful so we have to deal with it in the strongest way we can.
"It's a difficult social problem. I think there's a copycat thing: something happens and other people copy it and this sort of thing can spiral. To my mind it's for the FA, the whole game of football and the authorities to work together to deal with this most severe matter.
"I believe that if necessary these people need to go to the court and be banned for life, if they're found out.
"It's important that matters are brought to a head and people understand that there is no room for this in football at all, and we'll do everything we can within the FA. I know the rest of football feels the same, it's a blot on the game."