Police said the attackers - three white men and one Asian man - were racially motivated. The victims were black.
Protesters have been gathered since 25-year-old Jamar Clark was shot during a struggle with police on 15 November.
People who claimed to witness the incident said that Clark was handcuffed, though police dispute this.
Around two dozen tents and canopy shelters have been erected around the 4th Precinct police station. Demonstrators have also barricaded the roads with wood and pallets and lit campfires.
According to criminal complaints, the four men went to the camp on 23 November. After a group of protesters attempted to escort them away, eight shots were heard.
The city's mayor, Betsy Hodges, said the camp has become unsafe and has asked people to disband their week-long protest.
These request have been rejected by protesters, who have vowed to continue camping out despite cold weather and attacks. One of the shooting victims, Wesley Martin, said they refuse to leave.
"They can have the street. We can take the sidewalk," said Martin. "To be honest, we're not going nowhere."

The girl, named locally as Holly Hughes, is now in a stable condition after the crash involving a tanker and a van on the A44 in Powys on Tuesday.
Her mother mother Alison Hind, 28, died in the crash.
Ms Hind's uncle Martin Pugh, 47, and his partner's parents Margaret, 65, and John Kehoe, 72, were also killed.
Holly was flown to the University Hospital of Wales in Cardiff after the collision around 15 miles (24km) from Aberystwyth, near Eisteddfa Gurig, between the villages of Llangurig in Powys and Ponterwyd in Ceredigion.
The family's Ford Focus was travelling east on the A44, the transit van was driving behind it and the tanker was going in the opposite direction.
Local councillor Gareth Morgan described the incident as a "great tragedy" for the community.
He said the road was known to be one of the most dangerous in Wales and said the crash called for a major assessment of its dangers.
A Welsh government spokesperson said it was committed to doing all it could to make Wales' roads as safe as possible.

Its latest survey shows household spending dipped for the first time in four years last month with families "starting to feel the squeeze" as higher living costs eat into pay.
"Let's face it, we are skint," says commentator Justin Urquart-Stewart.
"Our card's maxed out, nothing in the savings account, pockets emptied out and nothing down the back of the sofa."
Visa said physical stores saw sales drop at their fastest pace for over five years in May, with sales down 5.3% year-on-year.
In contrast, spending at hotels and restaurants rose at an annual rate of 3.3%.
But even though so-called "experiences" spending rose, the figures suggest people are still being careful.
Josh Beer, from the Illustrious Pub Company, in Cambridgeshire, said: "More of our customers gravitated towards deals and offers in the past month, it feels as though they were biding their time, and cutting back until they became more confident in the economy."
The Visa figures show overall spending was 08% lower than in 2016, the first fall since September 2013.
The findings chime with official data from the Office for National Statistics, which shows that wage growth is falling back while inflation is rising, causing a squeeze on household incomes as they  fail to keep pace with shop prices.
The latest official figures showed wage growth behind inflation for the first time since mid-2014, and the Bank of England has said it expects this to get worse.
Average weekly earnings excluding bonuses increased by 2.1% in the three months to March, while inflation rose by 2.3% in the year to March 2017.
"Now is starts to hurt, with inflation above lower pay levels we will all start to feel poorer. As the consumer we have been the driver of the UK economic engine - and now you can hear it start to splutter," adds Mr Urquart-Stewart, co-founder of fund manager Seven Investment Management.
One of the chief reasons for inflation's rise is the steep fall in sterling since the UK voted to leave the European Union.
It is now worth between 11-15% less against the euro and the dollar, making anything we buy with our weaker currency more expensive.
That leaves shops with a dilemma, shred their often already paper-thin profit margins or raise prices.
Four men have been charged in a shooting at outside a Minneapolis police station that left five protesters wounded.
[NEXT_CONCEPT]
An 18-month-old girl who was the sole survivor of a crash which killed her mother and three relatives is improving in hospital, police have said.
[NEXT_CONCEPT]
We're buying fewer clothes and pairs of shoes, although we're eating out more, according to credit card firm Visa.