The club were made aware of the post on an unofficial Facebook page purporting to encourage 'banter' between fans of the Canaries and local rivals Ipswich this week.
Kick It Out have reported the comments to police as a hate crime and the club said in a statement they would work with both the campaign, the police and Ipswich to find the culprit.
The statement said: "The club has been made aware of racist language about our manager Chris Hughton posted on an unofficial fans' Facebook page in the last few days.
"Kick It Out.. has reported the comments made as a hate crime to the police and Norwich City totally supports this stance.
"We are in dialogue with Kick It Out and Ipswich Town and will co-operate fully with the police investigation into the incident.
"We have a zero tolerance policy on racism and all other forms of discrimination and any supporter found guilty of racial abuse faces a lifetime ban from Carrow Road in addition to any punishment handed out by the courts."