The attack on the protesters unfolded late Monday near a police precinct where dozens of protesters have been camped out since the November 15 fatal shooting of Jamar Clark. None suffered life-threatening injuries.
According to police, Clark was shot after he struggled with officers. But some people who said they saw the shooting said the 24-year-old was handcuffed.
The protests are linked to the Black Lives Matter movement which arose in response to a number of police killings of unarmed blacks in Ferguson, Missouri, New York and Baltimore.
Two more men both white, ages 26 and 21 turned themselves in Tuesday afternoon.
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Protesters said that before the shooting they noticed three men and a woman who seemed out of place and were asked to leave. Moments later, shots rang out about a block away.
"I really did think it was like firecrackers or something initially because it was so loud and there was like this acrid smell," protester Jie Wronski-Riley said. "I thought, 'Surely, they are not shooting at us.'"
It was not immediately clear who was behind the attack, but several racially disparaging comments had been posted on social media in recent days.
One video showed a white man brandishing a gun while claiming to be on his way to the protests. Police issued a warning Friday night, asking demonstrators to be vigilant and report any suspicious behavior to authorities.
Hennepin County Attorney Mike Freeman said it will be up to a grand jury to decide whether to bring charges against officers in Clark's death.
After marching from the Fourth Precinct police station in north Minneapolis, the site of constant protests since Clark was shot, to Minneapolis City Hall downtown, several hundred people gathered outside the police station Tuesday night for a concert.
The diverse crowd, which included a number of children, listened to hip-hop music and soul classics such as "A Change Is Gonna Come.