The incident took place in a popular fashion district and tourist area of Harajuku on Takeshita Street, near Meiji Shrine, in central Tokyo.
The narrow, iconic street is known worldwide as a hub of Japanese youth culture and fashion, and the area famous for its "Harajuku girls", who dress in outlandish, striking costumes.
Nine people were injured in the attack.
NHK World said the street, which had been closed to traffic, was packed with people paying a New Year's visit to the Meiji Shrine, which is supposed to bring good luck.
Among the victims, a teenager was seriously injured when Kusakabe rammed the rental vehicle with an Osaka license plate into the pedestrians.
One witness told NHK it was a "ghastly scene". Local media reported the student was in a coma.
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Meanwhile in Germany, police have detained a 50-year-old man on suspicion of ramming his vehicle into a crowd of people after midnight on New Year's Eve at a crowded plaza in the north-western town of Bottrop.
Tokyo Metropolitan Police told CNN that they have opened an investigation into the incident.
Police arrested Kazuhiro Kusakabe, 21, on suspicion of attempted murder.
Teenagers and adults in their 50s are among the victims, according to RT. One male university student remains in critical condition.
According to national broadcaster NHK, Kusakabe told police he was acting in "retribution for the death penalty" without giving more precise details.
A large tank filled with kerosene was found in the auto, police said. Traces of the liquid were also found on his clothes. Initially, a police spokesperson characterised the crash as an "act of terror", Reuters reported. In early July 2018, Japan executed 13 members of the Aum Shinrikyo sect that was responsible for the sarin gas attack in a Tokyo subway in 1995.