The 31-year-old, who has also been warned about his future conduct, sent the message to a Tottenham Hotspur fan after the London rivals drew 2-2 in the Premier League last month.
Cole had been fined the same amount for comments he made on Twitter in 2011 about England's friendly with Ghana.
"Following an Independent Regulatory Commission hearing today, Carlton Cole has been fined 20,000 pounds after he admitted breaching FA Rules in relation to social media," the FA said in a statement.
"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."
(Reporting by Toby Davis; editing by Alan Baldwin)
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