City have threatened to ban for life any Norwich fan found guilty of posting the abuse.
Police launched an investigation on Saturday after a number of supporters reported an offensive comment on an unofficial Facebook page.
It follows a similar incident earlier this month in which police said they were investigating a comment left on a social networking forum as a "hate crime".
The club said in a statement: "We can confirm that Norfolk police made us aware on Saturday of a new and separate incident of potential racist abuse aimed at Chris Hughton on an unofficial fans' Facebook page.
"As in the first and ongoing incident, we will co-operate fully with the police in their enquiries and we take it very seriously indeed, and if anyone is convicted of an offence in relation to these incidents, not only will they face whatever punishment is handed out by the courts, but they will also potentially face a life ban from Carrow Road from us."