"A small number of people are being treated for stab wounds", the statement said.
"The exact circumstances are yet to be determined".
The centre of Melbourne's CBD is in lock down.
Police at the scene in the Bourke St Mall. Only the soles of the person's feet were visible.
Witnesses said the man had parked a vehicle on Bourke Street, a busy shopping area in Australia's second-largest city, before it was seen in flames.
Melbourne's anti-terror sirens and loudspeakers are being used for the first time, sounding out across Bourke Street.
Police said the victims appeared to have been stabbed in the upper body.
A burnt vehicle is pictured at the crime scene following a stabbing incident in Melbourne on November 9, where one person was killed and two others injured in a rush hour stabbing incident.
According to police, the other two victims, aged 26 and 58, sustained non-life threatening injuries.
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He said: "Stranger and bystanders, who knew nobody involved, stepped in without a moment's hesitation.they too are people whose qualities make us all proud as well". The condition and injuries of the third person were not disclosed.
Australia's counter-terrorism command has taken a lead role in the investigation and police set up a three-block-wide exclusion zone as forensic investigators combed through the scene.
"Me and the managers ran out and that's when we saw the auto on fire and then we saw the guy on the floor and we wanted to help, there were two blokes helping him out already, he was face down pools of blood around his face", he said.
It was too early to say if the incident was terror-related, they said.
One witness, Sarah Krug said she was heading to the night noddle markets when "all hell broke loose".
The incident unfolded on a busy downtown street on Friday evening.
"I'm absolutely terrified", he said. The man follows with the trolley and pushes it towards the attacker again, as a police officer opens fire. Police response was swift and overwhelming.
Another witness said: "Big fire".
The street where the auto caught fire was the scene in January 2017 of a fatal incident in which a man drove his vehicle at pedestrians at high speed, killing six people and wounding about 30.
Police will investigate a possible copy-cat motive.