Huddersfield Town are investigating reports of homophobic chanting during Saturday's 2-1 home defeat by Brighton.
The weekend's Premier League matches marked the start of the Rainbow Laces campaign, which is a show of support for the LGBT community.
Huddersfield say any supporters proved to be involved in such chanting "will face banning orders".
"This is not something Huddersfield Town will allow or accept," a club statement read.
"It is totally abhorrent and an affront to the overwhelming majority of the club's fantastic supporters.
"Huddersfield Town is extremely proud of its reputation as an inclusive club and the behaviour of a few individuals will not be allowed to tarnish this."
Kirsty Clarke, director of sport for equality rights group Stonewall, said: "This is a reminder of why Stonewall's Rainbow Laces campaign is so important.
"Our research shows more than half of British people (58%) believe it's important anti-LGBT language is challenged at live sporting events.
"Rainbow Laces is about giving people the confidence to tackle this abuse and show their visible support for lesbian, gay, bi and trans people, on and off the pitch.
"We're now working with national governing bodies to help make sport more inclusive of LGBT people. The more players, fans, clubs and organisations that stand up for equality in sport, the sooner we kick discrimination out and make sport everyone's game."