The incident, in which the man drove into two bus shelters, killing one person and seriously injuring another, immediately drew comparisons with a string of attacks across Europe in which vehicles have been used as killing machines.
But investigators said there was no evidence of any terror links, saying the 35-year-old French driver who had a book about philosophy and another about Islam in the car, had "psychological" problems.
French forensic police search the site following the car-ramming incident in Marseille. AFP
The attack is one of a handful in the past month in France in which men suffering from mental illnesses have apparently mimicked jihadist assaults.
Collomb said that of the around 17,400 people flagged by the intelligence services as radicals one third were believed to be mentally ill.
The minister said he would enlist the help of psychiatric hospitals in identifying patients who represented a potential threat.
"The medical secret is sacred of course but at the same time we must find a way to avoid a certain number of individuals suffering from serious disorders carrying out attacks," he told BFMTV news channel.
Terrorism experts have long warned that the intense media coverage of jihadist violence could spur copycat attacks by mentally unstable individuals with a propensity for violence.
Citing the case of the Marseille driver, who had several convictions for violence and robbery, Collomb said: "It's not terrorism... but it is imitation".
On August 6, a knife-wielding 18-year-old on leave from a psychiatric hospital was arrested at the Eiffel Tower after bursting past security shouting "Allahu Akbar" (God is Greatest).
The man said during questioning that he had wanted to kill a soldier.
A week later, a 32-year-old man rammed his car into a pizzeria near Paris, killing a 13-year-old girl and injuring 13 people.
The man, who had taken large quantities of medication, told the police he wanted to commit suicide.
Collomb did not say how the authorities assessed the mental health of individuals on the watchlist.