A man was shot by police after setting his vehicle on fire and stabbing three people and killing one in the city's central business district. The area has been cordoned off and the public are urged to avoid the area.
When they arrived, they were allegedly confronted by a man who started lunging at them with a knife.
One of the injured was reportedly in suspected critical condition with a neck injury, while another had sustained a head injury.
The auto burst into flames before a man emerged and began attacking people in the street, police said.
Video shows the man attempting to slash police officers with a large knife before falling to the ground.
A series of videos have already surfaced online showing the series of events leading up to the moment a knife-wielding man was shot by police in Melbourne's CBD.
Footage from the scene show a man making stabbing gestures at two uniformed officers near a burning auto before he was shot.
It has now been confirmed one person has died.
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A bystander tries to assist police by ramming a shopping trolley between police and the suspect.
Victoria police declined to comment when contacted about Islamic State's claim.
"We don't believe there is an ongoing threat at this stage, but certainly we are treating it as a terrorism incident", Ashton said. But after reaching the spot they witnessed that several people were stabbed and critically injured.
"A man was arrested at the scene and has been taken to hospital under police guard in a critical condition", the statement said.
Mr Gaut then went back into the McDonalds, which was in lockdown for more than an hour, to pat the shoulder of a trembling witness recounting his account to police.
Superintendent David Clayton told the media at a press conference that "passersby were calling out that members of the public had been stabbed".
UPDATE: A MAN has been shot by police after setting a vehicle on fire and allegedly stabbing a number of people in Melbourne's Bourke St.
Memories remain fresh of a fatal but not terror-related attack on the same street a year ago, in which a man drove his auto at pedestrians at high speed, killing six people and wounding about 30.