Spokesman John Elder told The Associated Press in an email just before midnight Monday that none of the injuries are life-threatening.
The Star Tribune reported the shootings occurred near an alley about a block away from the 4th Precinct stationhouse, where protesters have been conducting a sit-in since the shooting of 24-year-old Jamar Clark on Nov. 15.
CBS Minnesota reports three of the victims were hospitalized.
Witnesses at the scene told the station the shooters were white supremacists and were hanging around the rally before being asked them to leave. The witnesses said the men came back a short time later and fired six shots at protesters.
A crowd gathered at the scene, and heated words were exchanged with responding officers, CBS Minnesota adds.
Authorities have said Clark, 24, was shot during a struggle with police after he interfered with paramedics who were trying to assist an assault victim. But some people who said they saw the shooting allege Clark was handcuffed.
Protesters, some from the group Black Lives Matter, and Clark’s family have been calling for investigators to release video of the shooting. The state Bureau of Criminal Apprehension said it has video from the ambulance, a mobile police camera and other sources, but none shows the event in its entirety. The agency, which is conducting a state investigation, said releasing the footage now would taint its probe.
The protesters are refusing to leave until the video is made public.
A federal criminal civil rights investigation is also underway to determine whether police intentionally violated Clark’s civil rights through excessive force.