Ms Damond was killed outside the home she shared with her fiance, Don Damond, and was preparing for their wedding in August.
The bride-to-be, who used her fiance’s surname despite not yet being married, wrote online that she was working as a spiritual healer and meditation coach, but was also a trained veterinarian.
Ms Damond was fatally shot in an alley behind her home at about 11.30pm on Saturday night.
Dressed in her pyjamas, the woman was talking to an officer in the driver’s seat of the police car when the officer in the passenger seat pulled out his gun and shot her through the driver’s side door, sources told the Star-Tribune.
The Minnesota Bureau of Criminal Apprehension (BCA), which is investigating the incident, said two officers responded to “a call of possible assault” when “at one point an officer fired their weapon, fatally striking a woman”.
The BCA added that the officers’ body cameras weren’t during on at the time of the incident and that they are investigating.
The squad car’s camera did not capture the incident in the 5100 block of Washburn Avenue South, in Minneapolis’ upscale Fulton neighbourhood.
Ms Damond’s family have demanded answers and the city’s mayor has said she was “deeply disturbed” by the incident.
The BCA said of its investigation: “More information will be available once initial interviews with incident participants and any witnesses are complete.
“The officers’ body cameras were not turned on at the time and the squad camera did not capture the incident.
“Investigators are attempting to determine whether any video of the incident exists.”
The two officers involved are on paid administrative leave, which is standard procedure following such an incident.
Ms Damond, originally from Sydney, also went by the name Justine Ruszczyk.
In the aftermath of the shooting, her 22-year-old stepson Zach, whose dad Don, 50, was due to marry her in August, released a video saying he wanted answers.
Her fiance was away on a business trip when she was killed.
Zach said in the video: “Basically, my mom’s dead because a police officer shot her for reasons I don’t know.
“I demand answers. If anybody can help, just call police and demand answers. I’m so done with all this violence.”
He said Ms Damond called 911 after hearing a sound in the alley.
Minneapolis Mayor Betsy Hodges told reporters that she has “questions about why the body cams weren’t on”.
She added: “I am heartsick and deeply disturbed by the fatal officer-involved shooting that happened last night. I know the neighborhood well.
“We have few facts at this point. I want to know more. I call on the BCA to share as much information with all of us as quickly as they can.
“I have questions about why the bodycams weren’t on.”
Hundreds of people gathered at the scene on Sunday to mourn Ms Damond.
A neighbour named Hannah, 21, told the Star-Tribune: “I don’t know what she was doing out.
“She’s such a kind woman. She took me in when I was in a tough situation and helped me with whatever I needed.”
She said of Ms Damond and her fiance Don: “They were just so in love. I’m just kind of in disbelief.”
Ms Damond described her work on her website, writing that she had studied and practiced yoga and meditation for more than 17 years.
Her website states: “Her interest in supporting people to heal and transform themselves developed after she saw family members suffer greatly from depression, alcoholism and cancer.
“After losing much of her family to cancer she has spent many years on a personal investigative journey to discover how habits and disease develop, and how people can change and live in joy, expressing their full potential.”