The 20-year-old is recovering from a serious knee injury sustained while on loan at Wolves.
After posting a message this morning on his official Twitter account which read "if you going church today Pray For me Giving today A Miss", the Gunners midfielder retweeted a response from one Tottenham fan which read: "I prayed you break your arms and legs", to which Frimpong replied "> Scum Yid".
The post was swiftly removed by Frimpong, but soon sparked great debate on the social network site among supporters from both Arsenal and Tottenham.
One was retweeted by Frimpong, 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 are aware of the matter, but were this evening making no official comment.
The term "Yid" or "Yiddo" has been used for decades to identify Tottenham supporters because of the proportion of Jewish supporters at the north London club.
Last year, comedian David Baddiel launched a campaign to stamp out use of the word "Yid" in football chants, which can be viewed as anti-Semitic.
However, many Spurs fans use the term "Yid army" themselves and claim they are not offended by it.
Arsenal were not available for comment when contacted by Press Association Sport.