A state agency is investigating the incident, which happened on Sunday morning.
Relatives of the man concerned said that he was on life support.
On Monday, Minneapolis Mayor, Betsy Hodges, called for a federal civil rights investigation into the case.
Several area Metro Police Departments were on scene attempting to control the situation.
According to the Minnesota State Patrol, protesters were given four warnings to disperse or be subject to arrest.
On Sunday about 150 people gathered to demonstrate at the scene of the shooting and some camped outside the police station.
The officer involved in the shooting has not been identified yet but two officers have been placed on paid leave.
Family members said Jamar Clark, 24, was shot in a scuffle with officers early on Sunday morning.
Police said that he was a suspect in a domestic assault and interfered with paramedics who responded to the scene.
Some witnesses alleged that Clark was handcuffed when he was shot.