The attacker was shot by police after confronting officers on a busy city street, authorities said.
Emergency services were called to a vehicle fire at the corner of Swanston and Bourke streets about 4.20pm on Friday.
In a statement police said a man was arrested at the scene and has been taken to hospital in critical condition.
Police said they were "not looking for anyone further at this early stage".
A total of three people were stabbed during the assault, police revealed during a press conference.
Ambulance Victoria said paramedics had assessed three people at the scene.
A second person has been taken to hospital with a head injury, however their condition is not yet known.
One of the victims has died, while the others have been taken to hospital.
Video uploaded onto social media shows the suspect running at two police officers with a large knife as the blue ute burns in the background.
'The exact circumstances are yet to be determined at this stage.
Police are urging people to avoid Swanston Street and Bourke Street.
Police officers at the scene on Bourke Street in Melbourne after a man attacked others with a knife.
Mr Hair said two civilians became involved as well as two police, trying to stop the man from his attack.
Another said they heard "what sounded like a bomb and gun shot".
Twitter user Meegan May wrote: "Guy seems to have set his auto on fire, then attacked police with a knife".
"A small number of people are being treated for stab wounds", the statement said. Police response was swift and overwhelming.
Victoria Police released a statement saying: "Police are now at an incident on Bourke Street in the CBD".
"And then I heard one loud bang".
It comes as a trial continues into the horrifying rampage in Bourke St in January past year.