Thirty-five officers were injured in clashes when marchers took to the streets on November 11 in defiance of pandemic restrictions, state news agency PAP reported.
Over 300 people were detained, according to public broadcaster Polish Radio.
After calls by top Polish politicians for participants to stay home amid a COVID-19 epidemic, the organisers of the annual Independence March had said it would take place in motorised form only this year.
Prosecutors are probing an incident "during which there was an active assault on police officers and a breach of public order involving throwing fireworks, glass bottles, stones and other dangerous objects at police officers," said Aleksandra Skrzyniarz, a spokeswoman for the District Prosecutor's Office in Warsaw.
Police have said that “hooligans” targeted officers, who responded by using rubber bullets and pepper spray.
Warsaw Mayor Rafał Trzaskowski 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.
Poland on Friday reported 24,051 new infections and 419 more deaths, bringing its total number of COVID-19 cases to 665,547 and fatalities to 9,499.