Authorities now say they are treating the attack as a terror-related.
The attacker, 31, was shot after confronting officers on a busy city street, authorities said. He was taken into custody in a critical condition.
The two survivors are in hospital, neither are in a serious condition. The suspect has not been named.
Police said they were “not looking for anyone further at this early stage”.
“We don’t believe there is an ongoing threat at this stage, but certainly we are treating it as a terrorism incident,” said Victoria Police Chief Commissioner Graham Ashton.
He said the suspect, who is of Somali origin, was “someone that is known” to both local police and federal intelligence, adding it was “mainly in respect to relatives” who are “certainly persons of interest to us”.
Somali-born Australian who set fire to a gas-laden truck in the centre of Melbourne and fatally stabbed one person before he was shot by police was inspired by Islamic State but did not have direct links with the group, Australian police said on Saturday.
In an attack described by the state premier as an “act of evil”, the man sped a utility vehicle down Bourke Street, one of the city’s busiest thoroughfares, and then stopped and apparently set it alight before randomly stabbing pedestrians.
A man aged 74, who had been stabbed in the face, died at the scene.
Two other men, aged 26 and 58, are in a hospital with non-life threatening injuries.
Islamic State of Iraq and the Levant (Isil) claimed responsibility for the attack.
Police identified the man responsible for Friday’s attack as 30-year-old Hassan Khalif Shire Ali, 31, whose 21-year-old brother was accused of plotting a mass murder on New Year’s Eve at Federation Square last year, a city centre hub and popular tourist spot. He is in jail awaiting trial.
Footage taken by witnesses showed the man lunging with a large knife at police, who shot him in the chest and killed him. Bystanders were yelling at police: “Just shoot him, just shoot him”.
Police said Shire Ali’s Australian passport was cancelled in 2015 after an intelligence report he planned to travel to Syria, but an assessment was made that whilst he had radical views, he posed no threat to national security.
“I think it is fair to say he (Shire Ali) was inspired. He was radicalised,” Australian Federal Police Acting Deputy Commissioner Ian McCartney told reporters in Melbourne.
“We’re not saying there was direct contact. We’re saying it was more from an inspiration perspective.”
Scott Morrison, the Australian Prime Minister, said the national terrorism advisory remained at “probable”, the midpoint of a five-tier system, and told reporters in Sydney that radical Islam was the issue.
“I need to call it out. Radical, violent, extremist Islam that opposes our very way of life. I am the first to protect religious freedom in this country, but that also means I must be the first to call out religious extremism,” he said.
Isil’s propaganda channel said the group was behind the attack.
“The perpetrator of the operation… in Melbourne… was an Islamic State fighter and carried out the operation… to target nationals of the coalition” fighting Isil, Amaq reported a jihadist security source as saying.