"Police initially responded to a report of a auto 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.
One person was dead at the scene and two others were taken to a hospital.
The man, who was originally from Somalia, was known to the police and the incident is being treated as terrorism, Victoria state police Commissioner Graham Ashton said.
"People who'd seen it had told me they heard shots being fired, and everyone heard an explosion that was like the petrol exploding".
Police appear to fire a single shot at the man before he falls to the ground just as more onlookers attempt to encircle the man, one male brandishing what appears to be a hubcap and another with a shopping trolley. Some witnesses said the vehicle exploded before the man began stabbing people.
Another of the victims has reportedly died in hospital care, while a third is fighting for life.More news: US midterms: Combative Trump blames media, fellow Republicans for House losses
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"A man was arrested at the scene and has been taken to hospital under police guard in a critical condition", the statement said.
A man has been arrested after setting a vehicle on fire and stabbing three people - one fatally - in central Melbourne, Australia. The militant group also claimed responsibility for a deadly siege in the city in 2017 when a Somali man was killed by police after taking a woman hostage.
Victoria premier Daniel Andrews urged the public to avoid the crime scene, and thanked responding police officers. The exact circumstances are yet to be determined at this stage.
Another terrified witness, Ben, called the radio station to say he saw a white sheet covering a body in the middle of the sidewalk. One of the injured was reportedly in suspected critical condition with a neck injury, while another had sustained a head injury.
Bourke Street is now blocked between Swanston and Russell streets, and people are being advised to avoid the area.
Mobile phone footage shows a man, wielding a weapon, attacking officers about 4.20pm.