Police fired tear gas and protesters threw rocks and sprayed graffiti on police cars.
Video of the death shows George Floyd, 46, groaning "I can't breathe" as a policeman kneels on his neck.
Four police officers have been fired, with the mayor saying that being black "should not be a death sentence".
The incident echoes the case of Eric Garner, who was placed in a police chokehold in New York in 2014. His death became a rallying call against police brutality and was a driving force in the Black Lives Matter movement.
