One of the injured is said to be in a serious condition. All three are thought to be of Chinese origin.
The incident occurred outside a college in the suburb of Blagnac.
French media quoted police sources as saying the incident was deliberate but the driver, reported to be aged 28, was not on a security watch list. He was arrested several minutes later.
Police say the man was being sought for previous minor offences, notably drugs-related.
Unconfirmed reports say he suffered from major psychological problems.
The injured students, said to be aged 22 and 23, have been taken to hospital in Toulouse.
The public prosecutor has visited the scene of the accident and for the moment there has been no suggestion that it is an act of terrorism.
Toulouse Mayor Jean-Luc Moudenc tweeted (in French): "Very shocked by the aggression towards the students in Blagnac. We offer all our support to them and their loved ones."