Speaking at a news conference, Chief Commissioner Graham Ashton said that the suspect had "family associations that were well known" to police and that he had been known to Australia's security agency.
Melbourne was also the scene of two fatal car-ramming incidents past year, but neither was linked by police to terrorism.
A auto was set on fire and a number of people were stabbed this afternoon before the knife-wielding man was shot by police.
This image made from video shows police on street corner after a shooting in Melbourne, Australia.
The suspect was was hospitalized in critical condition.
Police were initially called to an incident in Bourke street, right in the heart of Melbourne, after reports of smoke and a vehicle in flames.
"(Officers) were confronted by a male brandishing a knife and threatening them", Supt Clayton said.
About 4.31pm, police send out a media alert asking the public to avoid the Bourke Street area.
Major disruptions are expected in the CBD on Friday evening, as details of a major incident in Bourke Street emerge.
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Australia: One dead in Melbourne multiple stabbing attack
Witness Fiona told 3AW her friends had seen someone with a knife in the area and she'd been told he'd stabbed a security guard. Paramedics said they assessed three people at the scene, one with a neck injury: "They are in a suspected critical condition".
Police have since confirmed three people were stabbed, one fatally.
A small number of people have been treated for stab wounds.
The attacker also died half an hour after being taken to hospital under guard.
One witness told the Herald Sun that bystanders were calling to police, "shoot him, shoot him".
"Police are aware of an incident in the vicinity of Bourke Street", Victoria Police have said in a statement.
"We don't believe there is an ongoing threat at this stage, but certainly we are treating it as a terrorism incident", Ashton said.
Footage from the scene appears to show the man approach officers with the blade.
The area has since been cordoned off by the bomb squad. "They are in a suspected critical condition", they said. The attacker was shot by the police after setting a truck filled with gas cylinders on fire and is now in critical condition in the hospital.
Fully engulfed. Multiple loud bangs."This incident in Bourke Street comes on the second day of the highly-publicised murder trial of James Gargasoulas, who allegedly drove through Bourke Street Mall on January 20, 2017, killing six people and injuring 27 others".