The suspect allegedly stabbed Pavlos Fyssas, 34, shortly after midnight outside an Athens cafe.
A group of 15 men attacked the victim after an argument over football, police told the BBC.
Before Fyssas died, he identified his attacker.
The 45-year-old suspect, whose name is not being released, has admitted to supporting the neo-Nazi party Golden Dawn and confessed to the crime, police said.
The party denied any involvement in the killing, the BBC said.
Golden Dawn has been accused of frequent attacks against left-wing activists, but the party has gained support during the country's financial crisis.