The driver of the car, which today deliberately crashed into a crowd of pedestrians in central Melbourne, had mental health problems and was not linked to terrorism, police said.
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He is a 32-year-old Australian of Afghan descent who was known to the authorities and a drug user, according to Shane Patton, the chief of police of the state of Victoria.
"At this stage we have no evidence of any connection to terrorism," he said.
The incident occurred at 16:30 local time. Victorian State Police said the vehicle was a white Suzuki SUV.
Eyewitnesses said the car violated the red light at a busy intersection and crashed into a crowd of pedestrians at high speed.
An eyewitness told Melbourne radio station 3AW that he heard screams and saw people "flying in all directions".
The area was full of people doing their Christmas shopping.
The Victorian State Ambulance Service said a preschooler with a serious head injury was among the injured.
Police did not name the two detainees but photos taken on the spot and posted on social media show a bearded man in a flannel shirt sitting on the street talking to police.
An eyewitness told the Australian Broadcasting Corp that the vehicle was traveling at a speed of 80-100 km per hour.
"He did not appear to be braking or slowing down," said Jim Stupas, who was out of his shop at the time.
"All you heard was 'bang, bang, bang,'" he said.