Norwich have already begun an internal disciplinary procedure relating to the remarks, but the FA charge relates to a breach of FA Rule E3 - the use of abusive and/or insulting and/or threatening words in comments posted on a Twitter account.
Bennett had threatened two Arsenal fans taunting him on the social networking site after the 3-1 victory for the Gunner, tweeting: "If ya got a prob I'll finish you in a couple of seconds."
The England Under-21 international's Twitter page has been closed down.
Bennett, who joined Norwich from Peterborough last year, scored City's opening goal in their 2-1 win over Reading on Saturday.
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