The offending driver is in police custody after his car struck several people at the corner of Bourke and Swanston Street before hitting the other vehicles near Russell and Bourke Streets about 6pm on Friday, police said.
The driver, a 26-year-old man from Melton West, was arrested at the scene and taken into police custody, Superintendent Zorka Dunstan said, confirming a person in one of the hit cars had died.
"I can assure the community that there is no ongoing threat and the area will remain closed while the investigation continues," she said at the scene.
"At this early stage there's nothing to suggest any terror links."
Supt Dunstan said two officers who were nearby had quickly arrested the man who was sitting on top of his car.
She said he was known to police through "mental health interactions" and he was undergoing a mental health assessment on Friday night.
Online footage shows the driver being led away by police and at least three badly damaged cars at an intersection.
Supt Dunstan said three pedestrians who were hit at a tram stop were taken to hospital with minor injuries and two people in the other hit car also suffered minor injuries.
"We're just grateful that we had that quick arrest and there were no further injuries," she said.
Supt Dunstan said police were grateful to bystanders who came to the aid of the injured.
The streets of Melbourne were packed on Friday night ahead of Carlton's blockbuster AFL clash against Sydney at the MCG.
Many people were seen standing around the crash scene in apparent shock.
Six people were killed and dozens more injured after James Gargasoulas drove into a busy Bourke Street Mall in January 2017.
Bourke Street from Swanston Street through to Exhibition Street has been closed and people have been urged to avoid the area.
Yarra Trams has suspended all trams along Bourke and Swanston streets.
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