The 28-year-old driver, who was arrested immediately afterwards in the city's Blagnac suburb, "purposefully hit three people" on a crosswalk, Toulouse prosecutor Pierre-Yves Couilleau said.
The suspect, a single man who lives with his mother in Blagnac, had previously suffered severe psychiatric problems and was released from a court-ordered hospital stay in December 2016, the prosecutor said.
"What matters in this case is the psychiatric profile of the person," he added.
"The individual arrested immediately after the event said he had been planning this act for a month," the prosecutor said later in a statement.
When asked about the possibility the man was motivated by terrorism, the prosecutor said the attack was "nothing of that order".
The driver has had about 10 previous convictions for non-terror related crimes, he said.
The investigation is to be handled by regular judicial police rather than Paris's anti-terror unit, he added.
The victims are Chinese exchange students at the ICD-Toulouse International Business School. A 23-year-old woman was the most seriously injured, and two men aged 22 and 23 were also hurt and one of them remains in hospital, the prosecutor said.
The woman's life is not in danger, police said.
The attack occurred in front of the Blagnac campus of the Institute for Social Research, an AFP journalist said.
On Friday night, France's Interior Minister Gerard Collomb praised the police's response, saying "the investigation will determine the nature of his act".
The attack came days after China asked France to "ensure the security" of its nationals, who have been regular victims of thieves.
On November 2nd, a group of around 40 Chinese tourists were attacked with teargas and robbed outside a three-star hotel near Paris's Orly Airport.
On Friday a youth, 15 years old at the time of the attack, was sentenced in juvenile court to two years in prison for violently attacking and robbing a Chinese textile worker last year in the Paris suburb of Aubervilliers. The 49-year-old man died five days of his injuries.
France has also been the target of a series of vehicle attacks by extremists inspired by the Islamic State group.
In July last year, a Tunisian man ploughed a 19-tonne truck into a crowd in the southern city of Nice, killing 86 people.