Tear gas was fired by police, while protesters threw rocks and sprayed graffiti. Businesses were also looted.
George Floyd, 46, died on Monday and video showed him gasping for breath as a white policeman knelt on his neck.
There have also been protests in Chicago, Illinois, Los Angeles, California, and Memphis, Tennessee.
The renewed clashes on Wednesday came just hours after the city's mayor called for criminal charges to be brought against the policeman who was filmed pinning down Mr Floyd.
The four police officers involved in the arrest have been fired.