The Australian citizen of Afghan descent was driving alone when he crashed a white Suzuki Grand Vitara into pedestrians at high speed outside Flinders St Station on Thursday at 4.41pm.
He is under police guard in St Vincent's Hospital as police continue their "fluid investigation" into what they allege was a "deliberate act".
The man has been named as Saeed Noori by the Herald Sun, citing police sources.
Speaking on Thursday, Victoria Police acting chief commissioner Shane Patton said the driver was known to police for "historical assault matters" but was not on bail. He is yet to be interviewed.
An off-duty police officer has been singled out for praise by the Victorian Premier after his heroic response to the Melbourne horror.
Daniel Andrews said the off-duty officer who rushed in to arrest the 32-year-old man suspected of driving a car into busy afternoon crowds had selflessly come to the aid of others.
The officer, who has not been named, was injured and being treated in hospital, he said.
"I think we would be right to single him out for special praise for the way in which he instinctively came to the aid of others in the protection of public order and potentially avoiding so much other carnage."
Police believe the man driving has a history of mental illness and drug abuse. He was previously known to police.
Footage on social media shows police dragging the man from the car. Other videos show a young man being held down with officers checking his pulse while he appears to drift in and out of consciousness.
Nineteen were injured in the attack, including a preschool-aged child.
