The clashes began as some of the marchers - said to be members of far-right groups - broke away from the main rally and started to throw stones and flares at the police.
Several people were arrested, and there were reports of injuries.
It is the fourth year in a row that violence has erupted during the march.
Last year, a group of protesters tried to attack the Russian embassy.
On Tuesday, thousands of people took part in the annual march in Warsaw, which was initially noisy but peaceful.
The violence broke out when a group of people - many of them wearing masks - broke away from the main rally.
They hurled rocks, flares and paving slabs at police, who responded with water cannon.
One man was seen with blood coming from a wound to his head, according to Reuters news agency.
Earlier in the day, President Bronislaw Komorowski led official celebrations in the capital.
The march commemorates the day Poland regained its independence at the end of World War One in 1918.
Before that, Poland had been carved up between Russia, Prussia and the Austro-Hungarian empire.
Polish police have used water cannon to disperse hundreds of masked men during march marking National Independence Day in the capital, Warsaw.