All three students hit by the auto were Chinese, while the driver told police he rammed them "deliberately", local media said.
The prosecutor says the driver was known to police for about 10 minor crimes and not listed on a French register of people suspected of being radicalized by extremists.
The driver has a history of mental illness, the interior ministry said in a statement.
According to the police report, among the injured are Chinese students who are studying in the city. Two were taken to a hospital with injuries that were considered serious, but not life-threatening. La Dépêche du Midi newspaper quoted him as telling police he had heard voices telling him to harm someone.
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The 28-year-old driver, who was arrested immediately afterwards in the city's Blagnac suburb, "purposefully hit three people", and had been planning the attack for a month, Toulouse prosecutor Pierre-Yves Couilleau told news channel BFM TV.
A French police source told AFP that the attack was deliberate.
One hundred Chinese students were enrolled this year on an MBA course at the institute, the local paper said.