A state agency is investigating the incident, which happened on Sunday morning. Relatives of the man concerned say he is on life support.
On Monday, Minneapolis Mayor Betsy Hodges called for a federal civil rights investigation into the case.
Black Lives Matter protesters have been demonstrating in the city.
The group gained prominence after the police shooting of a black teenager in Ferguson, Missouri, in 2014.
That sparked protests nationwide about the police use of excessive force against African Americans.
Jamar Clark, 24, was shot after police were called to a reported assault, and police say he "interfered" with the paramedics assisting the assault victim.
Police officers have said "misinformation" is spreading about the Clark case, and some have told reporters he was not handcuffed.
On Sunday about 150 people gathered to demonstrate at the scene of the shooting and some camped out outside the police station.
The officer involved in the shooting has not been identified yet but two officers have been placed on paid leave.
Black Lives Matter organisers are demanding the release of any video footage that may exist of the altercation.
"We have been saying for a significant amount of time that Minneapolis is one bullet away from Ferguson," Jason Sole, chair of the Minneapolis chapter of the National Association for the Advancement of Colored People (NAACP), told Minnesota Public Radio.
"That bullet was fired last night. We want justice immediately."
Mr Clark has convictions for making terroristic threats, aggravated robbery and possessing a small amount of marijuana.
In 2013, Minneapolis police shot and killed 22-year-old black man Terrance Franklin, who was suspected of burglary.
Minneapolis is participating in a federal Justice Department programme for increasing trust between police and their communities.
Protests are ongoing in Minneapolis over the police shooting of a black man who witnesses say was unarmed and handcuffed at the time.