The AFP news agency cited a French police source who said the vehicle "deliberately" rammed a group of three students - two of whom were badly injured, and one who was not as seriously hurt.
The BFM news channel said the man was known to police for previous non-terror crimes and officers were checking reports he suffered from major psychological problems, AFP reported. The driver has been "maturing" the idea for about a month before the attack, he added.
Toulouse prosecutor Pierre-Yves Couilleau said: "The individual was known to the police and the judiciary for several offences".
A 23-year-old is more seriously injured, a young man and another girl, aged 22 and 23, have lighter injuries.
The woman's life is not in danger, police said.
The Blagnac campus of IGS, a chain of higher education institutions where the vehicle attack reportedly took place.
In the wake of the incident, Interior Minister Gerard Collomb tweeted that "Support for injured young people in Blagnac".
On November 2, a group of around 40 Chinese tourists were attacked with teargas and robbed outside a three-star hotel near Paris's Orly Airport.
Last summer, a Tunisian man used a large truck to kill 86 people in the southern French city of Nice.