Another woman driving a car panicked when she encountered a roadblock and ran over a protester, French Interior Minister Christophe Castaner said on Saturday on live television, Daily Sabah reported.
The accident took place in the town of Pont-de-Beauvoisin, to the North of the city of Grenoble in Southeastern France, according to the interior minister.
France was expecting a country-wide wave of protests Saturday.
Drivers started blocking roads across the country to protest rising fuel taxes, in a new challenge to embattled President Emmanuel Macron.
Protesters pledged to target tollbooths, roundabouts and the bypass that rings Paris on Saturday. The government is preparing to send police to remove protesters and threatening fines.
The taxes are part of Macron's strategy of weaning France off fossil fuels. Many drivers see them as emblematic of a presidency seen as disconnected from day-to-day economic difficulties.
The protesters have dubbed themselves the "Yellow Jackets" because they wear fluorescent vests that all French drivers must keep in their vehicles in case of car troubles.
Separately, ambulances briefly blocked Paris' Champs-Elysees on Friday to protest new rules on ambulance financing and put pressure on Macron's government.