Nine people were injured, one seriously, by the attacker who struck in the Harajuku fashion district shortly after midnight.
The street, which was sealed off to traffic, was packed with people heading to a shrine for New Year's prayers.
The man driving the car fled the scene but was later arrested by police for attempted murder.
The 21-year-old was identified as Kazuhiro Kusakabe.
Police told broadcaster NHK that he initially told them he had conducted a terrorist act, but then later claimed it was related to executions. It was not clear if he was referring to a specific execution or capital punishment in general.
Takeshita Street in Shibuya ward is a popular shopping area known for its quirky fashion and youth culture. It also attracts international tourists in large numbers.
NHK footage showed the van with a smashed front and paramedics carrying the injured on stretchers into ambulances.
Eight people were hit by the car with one of them, a male student in critical condition in hospital.
A ninth person was assaulted by the driver after he had gotten out of the car.
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