Frimpong responded to a comment made by a Tottenham fan on July 15 and although he soon removed the Tweet from the social networking site, it caught the attention of the FA.
The comment made by the Tottenham fan was retweeted by Frimpong, who also added the derogatory term that incurred the FA's wrath.
Frimpong made 14 appearances for Arsenal last season before joining Wolves in a spell that was cut short by a knee injury in February.
Arsenal last week confirmed the player had been "reminded of his responsibilities when representing the club".
On the same day the Premier League revealed new guidelines for social media by players, following consultation with the FA and the Professional Footballers' Association.