The Ghana-born player admitted to a charge of improper conduct over the comments, which included a "reference to faith", and was warned about his future conduct.
In a statement, the FA said: "Arsenal's Emmanuel Frimpong has been fined £6,000 and warned as to his future conduct after admitting an FA charge under FA Rule E3 for improper conduct in relation to recent comments made on Twitter.
"Frimpong posted comments amounting to improper conduct and/or which brought the game into disrepute, which included a reference to faith."
On July 15, Frimpong wrote on his official Twitter account: "if you going church today Pray For me Giving today A Miss."
But after a Tottenham fan responded by saying, "I prayed you break your arms and legs," Frimpong is said to have retweeted the message and allegedly replied with the derogatory term "yid".
His use of the insult, understood to be related to the large proportion of Jewish supporters of Tottenham Hotspur, sparked a debate among football fans on Twitter that caught the attention of the FA.
Frimpong was quick to remove the tweet and later said that he did not know the term used was offensive.
He tweeted: "Just wanna Say didn't even no the word is offensive as u hear it all the time but u live and learn from ur mistakes Have a gd afternoon (sic)"
Comedian David Baddiel launched a campaign last year to get the word used by Frimpong out of football chants as he views it as anti-Semitic and as serious as racial slurs.
Frimpong's charge also comes at a time when footballers are under the spotlight for their social media activity, including former England captain Rio Ferdinand recently being charged by the FA over his description of fellow player Ashley Cole as a "choc ice" on Twitter.