Her stepson Zach Damond, 22, said she called police after hearing a noise in the alleyway near their house in the suburb of Fulton.
"At one point an officer fired their weapon, fatally striking a woman," the police department said.
"Officers were dispatched. When officers responded, an officer-involved shooting occurred, which resulted in one adult female victim who is deceased and which has prompted our callout to the BCA [Bureau of Criminal Apprehension].
"The BCA will now further be conducting this investigation, this officer-involved shooting, from this point forward."
Minneapolis Mayor Betsy Hodges said in a statement that she was "heartsick and deeply disturbed by the incident".
"I'm seeking answers to the questions we all have, and will make sure to keep the communication flowing," she said.
Ms Hodges said she understood the police body cameras and squad camera, which were introduced to the Minneapolis Police Department last year, were not switched on when the shooting occurred.
The two officers involved have been placed on paid administrative leave, which is standard procedure.
A rally organised by local activist Mel Reeves was held at the site of the shooting, while other community members gathered for a vigil in Ms Damond's neighbourhood.
Local media say neighbours are mystified as to what occurred.
Zach Damond spoke at the vigil calling for more information and transparency from the authorities.
"Basically my mum is dead because a police officer shot her for reasons I don't know, and I demand answers," Mr Damond said.
"I just know that she heard a sound in the alley so she called the police, and the cops showed up.
"And she probably... thought something bad was happening and then the next thing, they take my best friend's life.
"I'm so done with all this violence, it's so much bullshit.
"America sucks, these cops need to be trained differently and I need to move out of here."
