The Gunners youngster made potentially offensive comments on Twitter in response to a Tottenham fan's jibe about his recovery from serious injury and could face action
The Gunners midfielder, who is currently recovering from a cruciate knee ligament injury sustained while on loan at Wolves last season, used potentially offensive language when in conversation with the rival supporter.
The 20-year-old posted on his page: "If you going church today Pray For me Giving today A Miss".
He then retweeted a response from a Tottenham fan reading: "I prayed you break your arms and legs", to which he replied: "@ Scum Yid".
The term 'Yid' is often used in connection with Tottenham fans and references an association with Jewish supporters at the north London club.
Although some fans use the term themselves, the term can be viewed as anti-Semitic and last year the comedian David Baddiel launched a campaign to end the use of the word in connection with Tottenham.
Frimpong soon removed the post, but the tweet instigated comments from both Arsenal and Spurs fans.
He retweeted one such response, which read: "You can't go around wanting players to break limbs, no matter who you play for. embarrassed to be a yid right now!"
The FA is aware of the matter but has made no official comment thus far.