Nacionalni Stroj had planned the rally as a protest against the southern province of Kosovo's demands for independence from Serbia.
The march was banned after protests by Jewish groups such as the World Jewish Congress (WJC) and some Serbian organisations.
About 5,000 anti-fascists had gathered in Novi Sad to protest against what they said was the rise of fascism in Serbia.
Thousands of riot police had been deployed to prevent the two groups from clashing.
One group of anti-fascists, who had passed by a Novi Sad cafe, were attacked with stones by Davidovic's men who were dressed in black shirts and military style boots.
Several people were hospitalised with injuries from hurled stones.
Cedomnir Jovanovic, the leader of Serbia's Liberal party and who attended the anti-fascist protest, said: "It is amazing that the police let those Nazi supporters gather on the streets of Novi Sad despite the ban."
Last month, the WJC said that the planned neo-Nazi rally was a "matter of great concern" for the organisation.
The Simon Wiesenthal Centre had said that the march was to mark the birthday of SS chief Heinrich Himmler and welcomed the decision to ban it.
Eight Bulgarians were arrested earlier on Sunday in Belgrade, after police said they were planning to travel to Novi Sad to join the march.