Another dramatic video shows two presumably plain-clothes police officers arresting the attacker after he was shot.
Superintendent David Clayton said officers responded to reports of the vehicle fire but were confronted by the man "brandishing a knife and threatening them".
Australian police said one person died at the scene and another two others were being treated for their injuries.
Police said there was no terrorism link at this stage but they are "keeping an open mind".
Commissioner Graham said the man had driven to the area at around 4:10pm this afternoon and deliberately started a fire in the vehicle before fleeing it.More news: Heathrow passengers delayed after runway lighting problem UK News
He thanked the Victoria Police officers involved and the members of the community who assisted.
"A second person has been taken to hospital with a head injury".
Police are treating it as a terrorist incident.
Police said they knew the identify of the suspect but declined to name him due to "operational reasons".
In total, three people were stabbed and one died at the scene.
Sky News Australia's Patrick Murrell said police had tried to "talk [the suspect] down and tried to use the Taser" before shooting him.More news: Thousand Oaks shooting victim, survivors lived through Vegas massacre
The man has been arrested and is under police guard in hospital.
"Respects to Trolley Man and also to those very calm cops who remained very professional and surely prevented more people from being injured", one person wrote online.
Appearing with police, Premier Daniel Andrews said "this is an evil, terrifying thing that's happened in our city and state today".
"It's the center of Melbourne, where a lot of the transportation changes over.it's probably the busiest part of Melbourne and late on a Friday", said Meegan May who witnessed part incident from a nearby tram.
"Police were still in the auto and the attacker came out to attack the police".
One witness told the Herald Sun that bystanders were calling to police, "shoot him, shoot him".More news: U-23 bowler Shiva Singh's 360-degree turn hogs limelight
Mr Hair said the assailant was dressed in Islamic clothing and of African appearance and about six foot four inches tall.