Barrow AFC have launched the investigation after being made aware of the remarks, which were made by a small number of spectators at the Cumbrian club's League Two fixture against Walsall on Tuesday night.
The club said the remarks referred to a Walsall fan who lost his life two months ago and said they did not reflect the opinions, thoughts or values of the club.
It said it would be working with the relevant authorities to monitor the situation.
A spokesman for Barrow AFC said: "Following last night’s Sky Bet League Two fixture against Walsall, we have been made aware of derogatory remarks from a small number of spectators that referred to a Walsall fan who tragically lost his life just two months ago.
"We must emphasise and remind everyone that these remarks do not reflect the opinions, thoughts or values of Barrow AFC, and we deplore any behaviour of its kind.
"As a result, we are working with the relevant authorities to monitor this situation going forward."