State-run Rossiya 24 showed large groups of bare-chested men with cropped hair running up to the entrance of the "Tornado" festival in the Urals city of Miass, some 1,400 km (850 miles) east of Moscow.
A spokeswoman said local police had no immediate comment on the motive for the attacks.
At least 60 people were killed in Russia last year in hate crimes, and 306 were injured, according to SOVA a rights group that racist violence in the country. Most were attacks on dark-skinned Muslim migrants from Central Asia.
Witnesses at the 3,000-strong festival said some of the men fired gunshots into crowds, Rossiya 24 said, and it showed policemen collecting axes and batons belonging to the skinheads.
Six of the 19 injured were taken to hospital, it said.
Ekho Moskvy radio station said the owner of a local cafe had been detained on suspicion of organizing the violence.
Activists in Russia warn that increasing xenophobia and a corrupt police force allow far-right groups to prosper.
