The Barclays Premier League club issued a statement saying the England Under-21 international had been the "subject of internal disciplinary procedures" in wake of the posts, which have now resulted in formal action from the governing body.
In a statement, the FA said: "Ryan Bennett has breached FA Rule E3 - use of abusive and/or insulting and/or threatening words in comments posted on a Twitter account.
"He has until 4pm on Friday 26 April to respond to the charge."
Bennett, who joined Norwich from Peterborough last year, scored City's opening goal in their 2-1 win over Reading on Saturday. His Twitter page has been closed down.
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