Police advised the public to avoid the Old Port area where the driver, a 35-year-old man, was arrested, Reuters reports.
"At the moment we have no information on the motives of this individual," a police official told Reuters.
The driver first hit a bus shelter around 08:15 in the 13th arrondissement - or district - in the poorer northern part of the city, before hitting a second bus shelter an hour later in the 11th arrondissement, several km south.
The incident comes as Spanish police hunt for the 22-year-old driver who plowed a van into a crowd in Barcelona on Thursday.
As UNIAN reported earlier, a 22-year-old driver plowed a rented van into a crowd in Barcelona's tourist spot, La Rambla, leaving a trail of dead and more than a hundred injured.
Last year, on France's Bastille Day, 84 people died when a 31-year-old Frenchman of a Tunisian man drove a truck into a festive crowd on the seafront Promenade des Anglais.