Norfolk Police are already investigating similar comments aimed at Hughton, 54, in the aftermath of last month's 1-0 win at Stoke City.
Anti-racism group Kick It Out had brought the initial comments to the attention of local officers.
A club statement confirmed they "will co-operate fully with investigations into these hate crimes and strongly supports prosecution of those responsible".
Chief executive David McNally added: "The club has a zero tolerance policy towards racism and other forms of discrimination and is committed to taking firm action against anyone found guilty of such behaviour on or off the pitch.
"There have been a number of examples of racist language being used about our players and manager in the past couple of seasons and enough is enough.
"Such language and behaviour is totally unacceptable and we will ban any supporter found guilty of racism from Carrow Road, in addition to any penalties which may be handed out by the courts.
"The message to any racists out there is simple - you are not wanted at Norwich City."
Norwich slipped to a 4-1 defeat to Arsenal on Saturday and sit 18th in the Premier League with seven points from their opening eight games.
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