Exeter say they have been made aware of a report of a "suspected discriminatory comment" from a crowd member aimed towards a Northampton player during Tuesday's Papa John's Trophy match at St James Park.
In a statement on their website, the Grecians said the remark was reported to the referee, who spoke to a player from each side and both managers.
Exeter added that they take "a zero-tolerance policy on this matter" and are "working with the police, Northampton Town and the match officials to get a better understanding of the incident and take the matter further".
A club spokesperson said: "The club works tirelessly to make sure that Exeter City is an inclusive and diverse club, and that St James Park is welcoming to everyone, regardless of race, identity, gender, sexual orientation or disability. Discrimination is not welcome at our club."
Northampton also released a statement, which read: "Northampton Town Football Club are aware of an alleged discriminatory comment made by a supporter towards one of our players at Tuesday's Papa John's Trophy tie with Exeter City.
"This was reported by our player to the match referee in the correct way so the matter can be investigated and we will continue to support that process with both the authorities and Exeter City Football Club.
"The player concerned has the club's complete support in this matter."