Adaisha Miller would have turned 25 on Monday, according to her mother, Yolanda McNair.
The shooting happened at an outdoor social gathering about 12:30 a.m., said police Sgt. Eren Stephens. It happened on the city's west side.
According to Stephens, the woman "embraced the officer from behind, causing the holstered weapon to accidently discharge." The bullet punctured Miller's lung and hit her heart, and she died at a hospital.
Stephens said the Detroit officer will remain on administrative duties while authorities investigate the shooting and report their findings to the Wayne County prosecutor. The officer's name was not released.
"For this to happen to her, whether they want to call it freak accident or mistake in judgment, it should have never happened to my child, and there's nothing I can do to get her back," McNair told WDIV-TV.
McNair said her daughter was out to mark her upcoming birthday.
"All she wanted to do was enjoy the weekend for her birthday," the mother said. "She had every right to enjoy turning 25 and look beyond that."