Local police said that passersby were “forced to jump out of the way” as the car approached the popular de Meir shopping street in Antwerp.
No one was injured, however, and the driver was taken away by police.
The prosecutor said the driver was a French national called Mohamed R, was born in 1977, and lived in France.
His car had French registration plates.
The Belgian prosecutor said police found a rifle and bladed weapons inside the car, although some media have reported that the rifle may have been non-lethal.
The incident comes one day after four people were killed in London after a man ploughed into passersby in the centre of the city, before killing a police officer with a knife.
That same day Belgium marked one year since the double bomb attacks in Brussels that left 32 dead.