The 26-year-old Melton West man is under police guard in the Royal Melbourne Hospital following the incident on Bourke Street on Friday night.
Victoria Police Chief Commissioner Shane Patton said the arrested man was not on bail and had no prior criminal history.
"He's effectively a cleanskin," Mr Patton told reporters on Saturday.
"Our only involvement was with a mental health transfer in 2020."
Detectives from the Homicide Squad have taken over the investigation into the crash, which killed a 76-year-old Brunswick man, but Mr Patton said there was nothing to indicate the incident was terror-related.
Video footage of the arrest shared on social media shows a man with long dark hair, wearing white pants and a white long-sleeved top and no shoes, sitting on top of a white Toyota sedan following the incident.
Mr Patton said the accused man's rantings while on the roof of the car would help determine whether the crash was intentional.
The vehicle is believed to have belonged to the driver's mother.
Police believe the car had accelerated after running down the pedestrians about 6.20pm on Friday.
"We are still working through to determine whether this is a deliberate or a reckless act," Mr Patton said.
Bourke Street was closed overnight, but has reopened after tow trucks early on Saturday removed a white Hyundai whose 76-year-old driver died in the crash, and a grey Mazda SUV - believed to be an Uber - from the scene.
Three pedestrians - a 26-year-old man from South Yarra, a 23-year-old woman from China and a 35-year-old woman from Docklands - were taken to hospital.
Two are in a stable condition and the other remains in a serious condition.
Two people travelling in the grey Mazda, aged 30 and 37 and both from Diggers Rest, were taken to hospital with minor injuries.
The streets of Melbourne were packed on Friday evening ahead of Carlton's AFL elimination final against Sydney at the MCG.
Premier Daniel Andrews expressed gratitude to bystanders who came to the aid of the injured.
"I wanted to, on behalf of all Victorians, thank those police members who very quickly and with great bravery did the most important work in terms of securing the scene and taking the suspect into custody," Mr Andrews told reporters.Â
"And finally, can I thank those many, many Victorians who were on the scene and who stayed and extended that hand of friendship and love to support and help the (injured) people."
He urged witnesses and anyone with dashcam footage to contact police.
Eyewitness Joey Tam was walking to the tram stop after finishing work when she heard people screaming.
"I heard a lot of people screaming, my natural instinct was to freeze,'" Ms Tam told the Today show on Nine.
"It's definitely shaken everyone up in the CBD."
She said the crash brought back memories for many Melburnians of other incidents in the same street in recent years.
Six people died and 27 were injured when James Gargasoulas ploughed into them after driving into Bourke Street Mall in 2017.
Friday night's deadly crash is not believed to be connected to any previous Bourke Street incidents.
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