The white BMW was seen being driven erratically on the Eastern Freeway at Doncaster in Melbourne's east early on Monday afternoon.
Police followed it into the CBD, where the SUV struck a woman on Exhibition Street.
She suffered non-life-threatening injuries and was taken to hospital for observation.
The car was dumped in Bourke Street Mall and the occupants fled on foot before being arrested outside a shopping centre on Lonsdale Street.
Two 17-year-olds and two 16-year-olds from the Bendigo and Yarra Ranges were arrested and charged with an array of offences, including theft of a motor vehicle, conduct endangering life, aggravated home invasion and theft.
One of the 17-year-old boys was bailed to appear in a children's court at a later date.
The other three are expected to face a children's court on Tuesday.
Premier Jacinta Allan praised police for quickly arresting the teens.
"This is disgraceful, dangerous behaviour. Victorians won't tolerate it and neither will we," she said in a statement after the incident.
Six people died and 27 were injured when James Gargasoulas drove into Bourke Street Mall in January 2017.
A driver rammed pedestrians crossing on the corner of Flinders and Elizabeth streets later that same year, killing an elderly man and injuring 17 others.
In November 2018, Hassan Khalif Shire Ali parked his ute on Bourke Street and set it alight before stabbing three people, killing Melbourne cafe owner Sisto Malaspina in a terror attack.
Victoria Police said no weapons were involved in Monday's incident and the car was believed to have been stolen from the Boroondara area on Sunday.
There were 28,482 motor vehicle thefts in Victoria over the year to the end of June 2025, according to the latest state crime statistics.
That equates to 78 thefts each day or one every 18 minutes.
Youth crime continues to rise in the state, with the number of offences committed by children aged 10 to 17 jumping 13.7 per cent year-on-year.
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