The Barclays Premier League club issued a statement on Tuesday night 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.
Bennett is understood to have been involved in some heated exchanges with football supporters on the micro-blogging site, responding to one following Norwich's defeat at Arsenal with "I'll finish you in a couple of seconds."
In his final posts before closing his account, the defender wrote: "Officially going to delete twitter! Seems you can't say what you want on here, public can say why they want bit seems I can't reply!
"Being charged by FA, for replying to someone coming for me, that's the reason so bye bye all."
Source: PA
Source: PA