A police spokesman said 23 officers and 24 other people were injured.
A mob of hundreds pelted police with rocks and fireworks. Officers responded with water cannons and rubber bullets.
The so-called Army of Patriots march drew tens of thousands to demonstrate in the Polish capital. Organizers tried to quell the unrest but were unable to prevent a two-hour melee outside the national stadium.
Police had deployed an extra 5,000 officers to keep order.
Police Independence Day observances have been marred by violence in the past.
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