Deona Knajdek, 31, was reportedly using her car to block a street for demonstrators when the other vehicle crashed into hers on Sunday night.
The suspect was detained at the scene by protesters and arrested by police. His motive was unclear.
Activists were demanding more official evidence in the killing of a black man.
Ms Knajdek died after being taken by ambulance to hospital. A second protester was injured and taken to hospital, said police.
Investigators said a preliminary investigation indicated the driver's suspected use of drugs or alcohol might be a contributing factor in the crash.
Ms Knajdek had posted a video on her Facebook page earlier on Sunday showing a peaceful protest with a handful of demonstrators at the Minneapolis intersection.
Hours earlier she shared an image with the slogan: "If we don't get it, shut it down!!!" On the Facebook page, she identified herself as a recovering addict and abuse survivor.
Ms Knajdek's mother, Debbie Kenney, visited the scene of the fatal collision on Monday.
"She wanted something to matter and she wanted black lives to matter and for this all to stop," Ms Kenney told the Star Tribune.
Ms Knajdek's brother, Garrett Knajdek, told the newspaper his sister "was using her car as a street blockade, and another vehicle struck her vehicle and her vehicle struck her".
He said his sister had returned to Minnesota from Georgia a year and a half ago to reunite with her two daughters, aged 11 and 13.
"She's such a wonderful person," the brother said. "She's had struggle and hard times, but she's always pulled out of it."
Protests have been ongoing in Minneapolis since the fatal shooting on 3 June of a black man, Winston Boogie Smith, by law enforcement.
US Marshals said they were trying to arrest Smith, 32, on a warrant for allegedly being a felon in possession of a gun.
They said the father-of-three was in a parked vehicle and produced a handgun, resulting in officers opening fire on him.
State investigators say there is no police camera footage capturing the killing; protesters are demanding more evidence.
Minneapolis was the epicentre of nationwide protests for racial justice after the police murder of George Floyd, an unarmed black man, on 25 May 2020.