The attacker was shot by police after confronting officers on a busy city street, authorities said.
"What we know so far about the individual. from what we know we are treating this as a terrorism incident", Ashton said.
Victorian Premier Daniel Andrews has praised both authorities and members of the public for their quick response in taking down the offender.
Shire Ali, who was shot by police and later died in hospital, was known to the Australian intelligence agency for three years.
The suspect died later in hospital. Police said then they believed he was an Islamic State sympathiser and was planning an attack Melbourne's central Federation Square on New Year's Eve in 2017.
Terror cult ISIS have claimed responsibility for the attack on social media insisting the knifeman was an "Islamic State fighter".
"A man was arrested at the scene and has been taken to hospital under police guard in a critical condition", police Superintendent David Clayton said.
One man charged at the tall attacker, who was wearing a long black shirt, with a shopping trolley just before police drew their weapons.
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Police had been called to the vehicle at 4.20pm Friday, local time, by which time the man had already started attacking bystanders.
Police were initially called to an incident in Bourke Street, right in the heart of Melbourne, after reports of smoke and a auto in flames.
Bourke Street reopened on Saturday morning, and a Reuters reporter said there was an increased police presence in the area.
The incident is being treated as terrorism, police said.
Ashton added that Counter Terrorism Command will investigate alongside Victoria police.
He said security for large upcoming public events, including commemorations for Remembrance Day on Sunday, would be reassessed and possibly boosted.
Police in Victoria have officially named the attacker behind the deadly stabbing in the Melborne CBD yesterday afternoon, identifying him as 31-year-old Mohamed Khalif, who was also known to go by the name of Hassan Shire.
Footage taken by witnesses showed police shooting the man after he threatened them with an object that appeared to be a knife.
"He was breathing and he was bleeding out".