Police arrested a 23-year-old white man, and two other white men, 21 and 26, turned themselves into police.
The search for additional suspects continues, they said in a news release.
"Officers and investigators worked nonstop throughout the night to develop suspects and leads," police said.
At one point Tuesday, Police had arrested a Hispanic man, but he was released after questioning.
Mayor Betsy Hodges said authorities were "sparing no efforts to find the suspects and bring them to justice."
"I abhor last night's attacks, They have no place in our city," she said. "I am committed to keeping out entire city and all of our people safe and together we will be one Minneapolis."
All five of those wounded were hospitalized late Monday with injuries that were not life-threatening.
The shootings did not occur at the protest, police spokesman John Elder said, but in "close proximity" to it.
Following news of the violence near the precinct, Clark's brother, Eddie Sutton, issued a statement thanking demonstrators for gathering in his sibling's honor but asking that they find other ways to protest his death, in light of the shootings.
"Thank you to the community for the incredible support you have shown for our family in this difficult time. We appreciate Black Lives Matter for holding it down and keeping the protests peaceful," Sutton said. "But in light of tonight's shootings, the family feels out of imminent concern for the safety of the occupiers, we must get the occupation of the 4th precinct ended and onto the next step."
Many of the protesters outside the 4th Precinct have been there the better part of a week, since the November 15 shooting involving two Minneapolis police officers and Clark, whom they were trying to arrest.
Details surrounding Clark's death have been murky, prompting demonstrators and the NAACP to call for the release of any video from the shooting of the 24-year-old African-American man.
Gov. Mark Dayton said Monday that the one video he has seen wasn't very helpful.
The camera gives a very narrow view out the back of an ambulance, Dayton said. Its focus is to show what would be taking place in the back of the vehicle, not outside it.
"It doesn't show anything that would be by any confirmation to one point of view or another," Dayton told reporters Monday.
Parts of the incident were recorded on several cameras, but no video shows the entire incident, said Drew Evans, superintendent of the Minnesota Department of Public Safety's Bureau of Criminal Apprehension. None of the videos will be released until the investigation is over.
The governor's description of the ambulance video provides some insight but adds little clarity.
"It's just a very brief fragment where Mr. Clark and one of the officers are encountering each other, and then they disappear from sight, and there is no other view of them until one of the officers after," Dayton said.
"There's no audio, but it appears after the shot was fired, one of the officers comes back into the camera view."
What the witnesses say
Several witnesses to the original shooting or immediate aftermath said the public needs to understand why the protesters are so angry. The witnesses are adamant that there was no reason for police to shoot Clark; they say he was restrained.
One said he is sure Clark was handcuffed. Another said he was unable to move.
"One of the cops had his knee in his back, and the other cop was kind of straddling him in an awkward type position," barber shop owner Teto Wilson said. "But they had complete control of him. I didn't see him fighting. I didn't seem him resisting."
Wilson said he had just walked out of the Elks Lodge as it was closing when he saw the officers with Clark on the ground. The lodge is across the street, about 35 feet from where the incident happened. It was dark, about 10 minutes before 1 a.m.
"I saw a still body laying on the ground restrained. Like I said, maybe about a minute after that, that's when the shot went off," he said. "There was no reason to shoot him."
Wilson said he couldn't see which officer shot Clark.
But Frederic Bruno, the attorney representing one of the officers, gave a different account.
"Mr. Clark was given multiple opportunities to desist," Bruno said in a statement.
"While he was being legally detained, he chose to resist, fight officers and to seize control of an officer's firearm," the attorney said. "At no time was Mr. Clark handcuffed, contrary to press reports and social chatter."
Minneapolis resident Everett Spicer, who said he saw Clark in cuffs, recoiled after hearing Bruno's statement.
"How (is) he going for a gun in handcuffs behind his back? Do you think I could see a gun back here?" Spicer said, putting both his hands behind his back as if being cuffed.
Spicer says he is sure of what he saw. He says he too was next door at the Elks Lodge and came out right after the gunshot went off.
"I instantly walked out the front door, and you see a man across the street in handcuffs on the ground. He wasn't moving. He wasn't twitching. He wasn't doing anything. The ambulance pulled off after they shot him," he said
Spicer said he was sure Clark was dead. Clark died at a hospital the next day.
Spicer said that as the second group of EMS workers came, police removed the handcuffs.
"They went back and took the handcuffs off because they didn't want the EMS team seeing that this man was still in handcuffs," he said. "He just shot him. That's more s*** you gotta deal with."
Union: Clark had control of gun
The police union has a starkly different version of events.
At a Thursday news conference, union President Robert Kroll said Clark had control of an officer's gun belt and pistol.
"It was in the holster, and he had physical control of the hand grip," Kroll said.
State and federal investigators are looking into the shooting.
Officers and paramedics were responding to a call of a woman being assaulted.
Kroll said Clark was trying to pull the woman out of the ambulance.
Authorities have said Clark was interfering with the woman's medical care when officers Mike Ringgenberg and Dustin Schwarze tried to arrest him.