Two other people are in hospital after being stabbed in a busy Bourke Street on Friday afternoon.
Videos shared on social media show a man attacking two police officers with an object, before he is subdued by police.
The officers were immediately confronted by a man brandishing a knife and threatening them.
Paramedics said they assessed three people at the scene, one with a neck injury: "They are in a suspected critical condition".
The spokesperson confirmed that one person had died in the stabbing attacks and that the attacker was in hospital.
According to them, the police initially responded to a report of a vehicle on fire near the corner of Swanston Street about 4.20 pm (10.50 am IST).
It is not yet known if the incident is terror related.
A man wielding a knife was shot by police.
In a statement police said a man was arrested at the scene and has been taken to hospital in critical condition.
Anyone with information or who witnessed the incident is asked to go to Melbourne West Police Station to make a statement.
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The exact circumstances are yet to be determined at this stage. "It's very early in the stages of the investigation", Supt Clayton said.
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.
They had initially thought the man was running to catch a tram close by, before a nearby police vehicle rushed to the scene.
Police have also urged the public to avoid the Street after witnesses describe a auto bursting into flames.
Another said they heard "what sounded like a bomb and gun shot".
"There's been an incident in the CBD near Bourke St", he tweeted.
'Police response was swift and overwhelming.
"I didn't know what was happening there was just so much chaos and screaming".
The Metropolitan Fire Brigade said the fire was contained within 10 minutes. "I heard at least one gunshot initially".
The apparent attack came as a 28-year-old James Gargasoulas underwent trial in Melbourne for driving into a crowd in the same area in 2017, killing six people.