A driver shouting the Islamic phrase "Allahu Akbar’’ (‘’God is great’’) in Arabic has run down pedestrians in the centre of the French city of Dijon, injuring 11, two seriously, French media reported.
He was arrested after targeting pedestrians in five different parts of the city in the space of half an hour.
He is said to be "apparently imbalanced" and to have spent time in a psychiatric hospital.
Witnesses told police the driver, aged around 40, had also said he was "acting for the children of Palestine".
France has the largest number of Muslims in western Europe - estimated at between five and six million.
There have been a number of "lone wolf" attacks by Islamists in recent years.
Last year, a convert to Islam stabbed a soldier in Paris.
The main suspect in the murder of four people at the Jewish museum in Brussels in May is a French-born man who spent a year fighting with jihadists in Syria.
In 2012, Mohammed Merah shot dead seven people, including a rabbi and three Jewish children, in the city of Toulouse before being killed himself in a police siege.
On Saturday, French police shot dead a man after he attacked them with a knife, also shouting "God is great".