The Daily Mail reports Bennett, 23, responded to the Arsenal fans' jibes after the Gunners' 3-1 win over Norwich by tweeting: "If ya got a prob I'll finish you in a couple of seconds."
On Tuesday night, after being disciplined by Norwich and reported to the FA, he tweeted: "Officially going to delete Twitter! Seems you can't say what you want on here."
A Norwich statement read: "Ryan Bennett has been the subject of internal disciplinary procedures following remarks made on the social media service Twitter.
"The club are waiting for further communication from the Football Association regarding any possible formal charge from them."