He was also warned about his future conduct and ordered to complete a compulsory education course. He must also pay costs for the hearing.
Assou-Ekotto was charged under FA rule E3, which relates to the use of social media.
Peter Griffiths QC, chairman of the FA Regulatory Commission, said: “Even though we have found that there was an aggravated breach of FA rule E3 we are satisfied that when the player sent the tweet on December 28, 2013, congratulating Anelka, in his mind he believed he was congratulating Anelka on what he perceived to be an anti-establishment gesture as opposed to one associated with antisemitism.
“But we are also satisfied of two further factors relevant to his culpability: That he was certainly aware before he sent the tweet that the quenelle gesture was very much associated with Dieudonne; and that he had, by then, acquired at least some knowledge of the controversies surrounding Dieudonne in the autumn of 2013, and that these had included, rightly or wrongly, allegations concerning antisemitism."
Assou-Ekotto has seven days to appeal.