According to the governing body, 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 the Canaries from Peterborough in January 2012, netted the opener in Saturday's 2-1 win over Reading.
He is understood to have been involved in exchanges with supporters on the micro-blogging site following Norwich's recent 3-1 defeat at Arsenal.
Norwich have already announced an internal investigation into the matter. Bennett's Twitter account has since been deactivated.