Federal authorities say the man was armed with a handgun and that agents fired after attempts were made to disarm him. He was later pronounced dead at the scene.
Local police have confirmed the man was a 37-year-old Minneapolis resident.
While his identity has not been publicly released, officials say he is believed to have been a US citizen and a lawful gun owner, with no serious criminal history.
Minneapolis police were not involved in the shooting itself but responded shortly afterwards.
Footage circulating online appears to show multiple agents restraining the man before gunshots are heard.
The video has fuelled widespread concern and renewed questions about the tactics used by federal immigration officers operating in residential neighbourhoods.
Authorities have urged the public not to draw conclusions until investigations are complete, but for many residents, the images have already deepened distrust.
The shooting comes amid a major federal immigration crackdown that has seen an increased presence of Immigration and Customs Enforcement and Border Patrol agents in Minnesota.
The operation has drawn fierce criticism from local leaders, who say it has escalated tensions and created dangerous situations for both residents and law enforcement.