Marseille's prosecutor Xavier Tarabeux said that investigators had "no element pointing to a terrorist attack" and that the driver was suffering from psychiatric problems.
"He was found with a letter from a psychiatric clinic and we are leaning towards treating it as a mental health case," Tarabeux told AFP.
The incident took place at around 9am, one source said, asking not to be named.
The Renault vehicle first drove at speed towards a bus stop in the city's 13th district, leaving one person seriously hurt, before targeting another stop in the 11th district, causing one fatality.
A body of a victim is evacuated to a waiting ambulance. AFP
Julien Ravier, mayor of the 11th and 12th districts, told BFMTV news channel that the victim was a woman in her 40s who was waiting alone at the stop.
The police source said the man was in his mid-30s and was not from Marseille. Another source said the vehicle was a van.
BFMTV reported that a bystander noted the registration number of the car, which the police used to trace the vehicle to the city's Old Port district, where the suspect was arrested.
Police sealed off the port area and urged residents in a tweet to avoid the neighbourhood which is popular with tourists.
The incident comes as police across Europe search for the driver of a van that mowed down pedestrians in Barcelona last week, killing 13.
France has also seen a series of terror attacks over the past two years, including several in which vehicles were used as weapons.
French forensic police officers search a vehicle. AFP
On July 14th 2016, an extremist drove a truck into crowds celebrating Bastille Day in Nice, killing 86. The driver was shot dead by police, and Isis claimed responsibility.
Further car attacks have targeted police and security forces. In June, an armed man crashed a car into a police van on the iconic Champs Elysees in what was described as an "attempted terror attack", and on August 9th, a man drove a car into a group of anti-terror soldiers in a western Paris suburb, injuring six.
Less than a week later, a 13-year-old girl was killed when a man deliberately drove a car into a pizzeria in a town east of Paris, badly injuring four other people. In that case, however, police were quick to rule out a link to terrorism, instead suggesting the attack was a suicide attempt. It later emerged the driver had consumed “large quantities of medication” before driving into the restaurant.
Terrorism experts have warned that the intense media coverage of the violence could spur copycat attacks by people with mental health problems and a propensity for violence.