The charge is thought to relate to a response from Cole to a tweet he received in the aftermath of West Ham's 2-2 draw against Tottenham last month, in which Sam Allardyce's side surrendered a two-goal lead.
The Twitter post, which was later deleted, was deemed to have fallen foul of FA rules and the governing body has subsequently decided to act on the matter.
An FA statement released on Thursday read: "The West Ham United player, who was also severely warned as to his future conduct, admitted posting a comment on his Twitter account which was abusive and/or insulting and/or improper and/or brought the game into disrepute, in breach of FA Rule E3."
It is not the first time that Cole has been punished for a comment made on social media.
The forward was fined the same amount in May 2011 after a tweet sent during an England friendly against Ghana.
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