Following City's 1-0 win at Stoke last weekend, what the club describe as "unacceptable terminology" was used on an unofficial fans' Facebook page popular with supporters of both Norwich and local rivals Ipswich Town.
Anti-racism campaign Kick It Out - who have reported the comments as a hate crime to the Police - said in a statement: "Kick It Out was informed of a racist message posted about Norwich City manager Chris Hughton on an unofficial fans' Facebook page on Sunday (29 September), and instantly brought the incident to the attention of the Police.
"The high level of abusive and discriminatory messages being posted on social media platforms is a growing concern for Kick It Out.
"Social media users at all levels of the game can assist in reporting incidents they witness online by informing the authorities via True Vision's website - http://www.report-it.org.uk/your_police_force."
A statement on the Norwich website said: "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 racist abuse faces a lifetime ban from Carrow Road in addition to any punishment handed out by the courts."