The demonstrator, a woman in her 50s, was killed at a protest roadblock in Pont-de-Beauvoisin in south-east France.
The driver of the vehicle that hit her, a woman taking her daughter to visit the doctor, panicked when the protesters started hitting her car and drove into the crowd.
She is in detention and is a state of shock.
Update 1.45pm French time
At least 47 people have been injured, three of them seriously, on the Yellow Vests protests by 1.45pm Paris time, according to Interior Minister Christophe Castaner.
A 71-year-old demonstrator was hospitalised in a serious condition after being hit by a motorist in Arras, northern France.
His life was reportedly not in danger.
Twenty-four people were arrested, 17 of them being detained.
About 2,000 demonstrations, mostly roadblocks, had been counted across the country.
Organisers had not notified the police about the demonstration, as is the case for many of the hundreds taking place on Saturday.
Castaner claimed there was another serious accident near the eastern town of Sélestat but local officials said the victim, a 45-year-old woman, was not badly hurt.
Her ankle was injured when a motorist drove over her foot, they said.
Driver arrested in Grasse, Nice Matin
Other reported injuries were:
- A driver was arrested in Grasse, in the French Alps, after trying to drive through a roadblock, slightly injuring a police officer;
- Two demonstrators suffered slight injuries in Grande-Synthe, north-west France, on Friday night;
- A driver was arrested after trying mounting the pavement to force his way through a roadblock in Hazebrouk, in the north-west, injuring to protesters;
- A driver was arrested after slightly injuring a woman demonstrator in Capendu, south-west France;
- A driver was arrested in Cuers, south-east France, after slightly injuring a demonstrator at an undeclared roadblock outside a supermarket.
Many of the demonstrations have not been notified to the authorities, creating difficulties in policing them and in assessing their number.
"We are at a maximum level of concern," Castaner said after consulting préfets across the country in a video-conference on Saturday morning.
Media reported more than 50,000 people taking part in more than 1,000 demonstrations across the country on Saturday morning.