The 21-year-old spent loan spells with Wolves, Charlton and most recently Fulham, before returning to the Gunners in the summer.
The Ghana international has, though, yet to appear for Arsene Wenger's side this season - something he implied on Twitter was because of his colour and nationality.
Asked on Monday night why he was not involved in Tuesday's Capital One Cup tie with Chelsea, he posted "LOL I wanna laugh", and then added: "Sometimes I wish I was white and English #realtalk."
Frimpong quickly deleted the comments and insisted: "Not every tweet is football related."
The defensive midfielder, who was last year fined £6,000 by the Football Association for branding a Twitter user "scum yid", later added: "Look what ever you read tomorrow has majorly been twisted. Is a joke what people will do to start controversy goodnight people."
Arsenal had no official comment on the matter when contacted by Press Association Sport, but it is understood the club will remind Frimpong of his responsibilities.
The midfielder has almost 800,000 followers on Twitter, a YouTube channel and official website, despite having started just three Premier League matches for his boyhood club.
Wenger said Frimpong's omission from the Arsenal squad to face Chelsea was because "he is still short of competition".