One steward was knocked unconscious and taken to hospital before being discharged.
"In reaching its decision the Commission took into account his admission of the charge, public apology and the extremely provocative nature of the abuse he received," read an FA statement.
"However, the commission also stated that players have a responsibility to conduct themselves in a proper manner and that such celebrations are unacceptable and have the potential to cause a serious public order incident."
Adebayor's suspended two-match ban will only be activated if there is a similar breach of FA rules before December 2010.
In the meantime, the Togo international is free to face Aston Villa in the Premier League on Monday after serving his three-game ban for stamping on Van Persie.
"Manu was in great form before his suspension and having him available again is a huge boost to us," said Hughes, whose side have made an impressive start to the season.
City lie fifth in the Premier League table, just three points behind leaders Manchester United and with a game in hand.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.