The man follows with the trolley and pushes it towards the attacker again, as a police officer opens fire.
The incident, which brought central Melbourne to a standstill in the late afternoon rush, came after police responded to reports of a burning vehicle. The reason for the attack has yet to be confirmed.
Footage from the scene shows a man earlier swinging a knife at two uniformed officers near a burning auto before he was shot.
A bystander in Bourke St said that a auto had burst into flames.
One of the stabbing victims died at the scene while two are in hospital. Police are not looking for anyone further at this early stage.
The knifeman then set fire to his vehicle before exiting to stab three people.
Local ambulatory authorities said three people were assessed at the scene, according to News.com.au.
In multiple videos that surfaced, a man can be seen trying to stab two policemen who try to make several attempts to wrest the knife from the man.
Two victims are still in hospital with non-life-threatening injuries. One person has been taken to hospital with a neck injury in a suspected critical condition, one with a head injury and a third with unknown injuries.
Ashton said the authorities do not see any ongoing threat related to the attack.
Dramatic footage showed two police officers trying to arrest the man as he lunges and slashes wildly in broad daylight on Bourke Street with his vehicle burning in the background.
Police had been called to the vehicle at 4.20pm local time on Friday, by which point the man had already started attacking bystanders.
"At the same time passers-by were calling out that members of the public had been stabbed", he added.
"I didn't know what was happening there was just so much chaos and screaming".
"A moment later, I heard a loud bang, to me it sounded like a gunshot", she said.
Another bystander told AAP he was walking on Swanston Street when he heard an explosion and then saw a "big dude punching into the police car".
"The one who executed the ramming and stabbing operation in Melbourne (.) is one of the fighters of the Islamic State and he executed the operation in response to (a call) to target the citizens of the coalition", Amaq said.
The bomb squad has cordoned off the area.