Police said “hooligans” hurled stones and flares at officers, who responded by using rubber bullets and pepper spray.
The onet.pl website reported that several thousand took to the streets in central Warsaw, even though the organisers of the annual Independence March had said it would take place in motorised form this year.
Police said that a number of people had been detained, adding: "In order to restore order, means of direct coercion are being used.”
Firefighters said that a blaze which broke out in an apartment in the centre of the capital had probably been caused by demonstrators throwing flares and fireworks as they marched past.
Warsaw Mayor Rafał Trzaskowski last week refused to authorise the march, which in the past has been criticised by liberals for attracting far-right troublemakers, but praised by conservative politicians as a show of Polish patriotism.
Polish Prime Minister Mateusz Morawiecki last week appealed for the Independence March to be called off amid a surge in COVID-19 infections.
Gatherings of more than five people have been forbidden in Poland under rules aiming to curb the spread of the coronavirus, and the government has warned that a nationwide lockdown may be imposed if cases continue to surge.
In a televised address, President Andrzej Duda on Wednesday told Poles that abiding by government restrictions was a form of patriotism.
Earlier in the day, the president and prime minister laid a wreath in front of the Tomb of the Unknown Soldier in central Warsaw during pared-back ceremonies to mark Independence Day.
Poland on Wednesday reported 25,221 new coronavirus infections and 430 more deaths, bringing its total number of cases to 618,813 and fatalities to 8,805.
Source: IAR/Polish Radio/onet.pl