Video footage taken by passersby and posted online shows the green four-wheel drive reversing at speed down Swanston Street in the CBD before spinning 180 degrees.
A member of the public threw a hire bike under the 4WD to try to stop it, while police rushed to the area.
Officers say they are treating it as a mental health situation and don't believe there was any terrorist links.
The teenager was wearing a black armoured uniform, black helmet and carrying a black rucksack.
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He got out of the vehicle and was pacing in circles at the corner of Swanston and Flinders streets when police surrounded him shortly before 8am.
He appeared to lunge at one of the officers, who fell back, before the teen was tasered and subdued.
No injuries were reported and the teenager was arrested and is in police custody.
The Bomb Response Unit were searching the 4WD as a precaution and the area has been cordoned off.
"He was driving certainly erratically which is concerning to Victoria Police and the community but there is no intention, that I'm aware of, that he was deliberately trying to hurt anyone," he said.
"Obviously it was concerning but this paraphernalia he had is freely available, the clothing [was] certainly from any army disposal store but obviously [being] in the CBD dressed like that is of concern, but I think that's clearly in line with his mental health condition which we're assessing."
Police are urging people to avoid the area.
It comes as thousands pack the area for the AFL grand final between Richmond and Adelaide.
