The 23-year-old was the subject of an internal investigation by the Canaries after allegedly threatening to "finish" two fans who abused him online.
It is believed that two Arsenal supporters taunted the defender following the Gunners' 3-1 victory over Norwich a fortnight ago.
According to the Daily Mail, Bennett responded by saying: "Listen how about stop being a melon n shhh if ya got a prob I'll finish you in a couple of seconds."
The FA released a statement, which said: "Bennett has breached FA Rule E3 - Use of abusive and/or insulting and/or threatening words in comments posted on a Twitter account."
Bennett, who deleted his account shortly after the messages, has until 4pm on Friday to respond to the charge.