Minneapolis police reported that the woman was critically injured in the incident and died later at a hospital. Three other people also sought medical treatment for injuries that were not life-threatening.
The driver was pulled from his vehicle by other protesters and assaulted before being taken into police custody. The driver is not being identified by police.
The victim was confirmed to be 31-year-old Deona Knajdek by her brother Garrett Knajdek, who spoke to KARE-TV.
"She was probably the most wonderful person you could ever imagine," he said. "She would ... tear the shirt off her back to make sure someone was warm."
He also told the Star Tribune that Knajdek had been using her car as a blockade when the car struck her vehicle and her own vehicle hit her.
Police would not comment on the possible motivation of the driver, but the Star Tribune reported that the use of drugs or alcohol might have contributed to the incident.
Looting and vandalism were reported at the Minneapolis protests, and on Monday one woman was arrested after shots rang out.
Garrett Knajdek also said that his sister, Deona, a mother of two daughters, would not have wanted any further violence in response to her death.
"She wouldn't want people rioting in the streets and causing chaos," he said. "She doesn't want a mess. She always wanted to make sure people were heard peacefully."
Here's a local news report about the lethal incident:
Woman killed after car drives into crowd of protesters in Uptownwww.youtube.com