The man was shot in the chest by police.
The attacker is in hospital in a critical condition and investigators have not released any information about his identity.
Police had been called to the vehicle at 4.20pm Friday, local time, by which time the man had already started attacking bystanders.
Chilling footage uploaded to social media shows the suspect repeatedly swinging the weapon at two officers before one of them draws their firearm and opens fire.
"Police initially responded to a report of a vehicle on fire. a man was arrested at the scene and has been taken to hospital under police guard in a critical condition", Victoria state police said in a statement.
Police are telling all members of the public to avoid the CBD, although dozens of witnesses are being interviewed by officers at the scene.
They said the suspect, who was hospitalised in a critical condition, had no known links to terrorism.
The attacker was shot by police after confronting officers on a busy city street, authorities said.
It is not yet clear whether he deliberately set the vehicle on fire but Mr Ashton said the auto had been laden with gas cylinders.
It was brought under control within about five minutes, a Metropolitan Fire Brigade spokeswoman said.
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Moments earlier, a auto burst into flames on the busy strip about 4.20pm.
May said she was taking the tram into the city center when she heard someone shout "he has a knife".
"Cops trying to take down man armed with knife".
'He seemed to be waving something, people around me screamed that he had a knife, but I couldn't see clearly from where I was, ' Michelle told ABC radio.
"I kept watching", said witness Tony Nguyen, after what he described as a "car bomb".
At one point, the man is knocked off his feet.
"He was facedown, facedown, and there was a lot of blood".
'I was already stepping on his blood'. "They didn't know what to do because obviously in that situation it is pretty insane".
A witness filmed the horrifying scenes as the attacker tried to thrust his knife towards police on Bourke Street.
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