A statement on the City website confirmed that the 22-year-old has been fined a total of 8 weeks' wages, including 2 weeks carried over from a suspended fine following a disciplinary hearing last December.
The midfielder has also agreed to undertake a programme of rehabilitation in a bid to prevent incidents of this kind occurring again.
City spokesman Paul Tyrrell said on the City website: "Joey has expressed his deep and sincere remorse over the incident and is keen to make amends to this football club and our fans, who expect the highest standard of behaviour from our players.
"He has apologised to those involved and has accepted his fine unquestioningly."
Barton added: "I understand the distress I have caused to everybody concerned and want to apologise for my actions. I am grateful for the support I have received from the club, and my friends and family."