Marches by far-right nationalists have been growing in size on the national holiday, with left-wing activists turning out to oppose them.
Police used water cannon and pepper spray to bring the situation under control.
They responded after right-wing marchers, many with scarves hiding their faces, began pelting them with stones, bottles and flares, national police spokesman Mariusz Sokolowski said.
The police were attempting to keep the nationalist and leftist demonstrators apart.
Nine police officers were injured, including three who were hospitalized with serious injuries, according to Mr Sokolowski.
Rightist demonstrators later set fire to a television van covering the unrest.
Earlier in the day, leftist demonstrators chanting “Fascism will not pass” attacked police as they tried to stop them blocking a major Warsaw thoroughfare, down which the nationalist march was due to pass, Mariusz Sokolowski said.
For weeks, a coalition of leftists, anarchists, pro-abortionists, Greens and gay-rights activists had been publicising plans to block the Independence March being organized by nationalist youth groups All-Polish Youth and the National Radical Camp, Reuters news agency reported.
A spokesman for Prime Minister Donald Tusk said he vowed to make sure those arrested for attacking police were severely punished.
Under Polish law, an assault on a law-enforcement officer carries a maximum three-year jail sentence.
The 11 November celebration marks the day in 1918 when Poland regained its independence, 123 years after it was divided between Russia, Prussia and the Austrian Empire.
Speaking at an official Independence Day ceremony earlier, President Bronislaw Komorowski had urged Poles to “celebrate this patriotic occasion together, not against one another”.
President Komorowski honoured fallen veterans by laying a wreath at the Tomb of the Unknown Soldier during state ceremonies.
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