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.
What happened at the protests?
They began in the afternoon on Tuesday, when hundreds of people came to the intersection where the incident had taken place on Monday evening.
Organisers tried to keep the protest peaceful and maintain coronavirus social distancing, with demonstrators chanting "I can't breathe," and "It could've been me".
Protester Anita Murray told the Washington Post: "It's scary to come down here in the middle of the pandemic, but how could I stay away?"
A crowd of hundreds later marched to the 3rd Precinct, where the officers involved in the death are thought to have worked.
Squad cars were sprayed with graffiti and protesters threw stones at the police building. Police fired tear gas, flash grenades and foam projectiles.