Police advised the public to avoid the Old Port area where the driver, a 35-year-old man, was arrested.
A source close to the investigation told Reuters the suspect was known to police for minor crimes and had psychological issues. France's counter-terrorism prosecutor said it had not taken up the case at this stage.
"The arrest was made in a surprisingly calm fashion, no gunshots were exchanged," David Reverdy, of the Alliance police union in Marseille, told BFM TV.
"The distance travelled by the driver suggests a certain determination," Reverdy said.
"But we can ask ourselves: why these places? If one wanted to cause carnage, other places in Marseille, at another time of day, would have been more logical," he said.
France has been under a state of emergency since Islamist militants killed 130 people in and around Paris in November 2015. Another 86 people were killed in an attack in Nice in July last year, when a Tunisian man drove a truck along the seafront boulevard, mowing down Bastille Day revellers.