Police spokesman Mariusz Sokolowski said three of those arrested Monday are suspected of setting fire to a guard's hut outside the Russian Embassy and another was suspected of setting fire to an art installation of a rainbow, considered a symbol of tolerance of homosexuality, TheNews.pl reported.
A dozen police officers were injured in the clashes.
"We are going to analyze footage from many surveillance cameras, so as to reach other people who might have been involved in something," Sokolowski said. "Police used service batons, pepper spray and smooth-bore weapons with rubber bullets."
Prime Minister Donald Tusk said efforts to organize similar marches in future may be curtailed.
"This situation is unacceptable," Tusk said. "This kind of event cannot take place. Those who tolerate and accept such events will bear responsibility."
Artur Zawisza, one of the organizers of the far-right march, said, "No piece of paper from the Town Hall will stop us marching towards independence."
Wojciech Zajaczkowski, Poland's ambassador in Moscow, was summoned to Russia's Ministry of Foreign Affairs in the wake of Monday's attack, TheNews.pl said.
The Polish Ministry of Foreign Affairs, in a statement, condemned the attack on the guard hut and expressed "deep regret at the violent behavior and incidents that took place at the Embassy of the Russian Federation in Warsaw."
RIA Novosti said the Russian Foreign Ministry would seek compensation for damages sustained at its diplomatic compound. Russian officials said the embassy gates and a sentry post were set on fire.