He is suspected of intentionally trying to kill people by driving the small vehicle through the street.
Kusakabe told the police he had meant to kill the pedestrians he hit "in retaliation for an execution".
"I can't believe it, this is a place I'm familiar with, so it's very shocking", said Tatsuhiro Yaegashi, a 27-year-old worker in the area.
Kyodo News Service reported that a ninth person was injured and that the driver was arrested on suspicion of attempted murder.
One college student suffered serious injuries during the attack and was undergoing surgery, the police spokesperson told AFP.
The street, which was sealed off to traffic, was packed with people heading to a shrine for New Year's prayers.
Kusakabe fled the scene, but the police found him in a nearby park about half an hour later.
No further details about the attacker's identity have been provided.
TV Asahi said officers were investigating whether the suspect is fit for trial.
Takeshita Dori is closed to traffic and is often tightly packed with fashionistas and global tourists.
Japanese media reports that a young man in his 20's drove a rented minivan into a busy street shortly after revelers had rung in the New Year.
There is no major fireworks display and no central point where revellers gather.
By midday Tuesday, hundreds of thousands of tourists had returned to the street filled with bright pink ornaments, although blue tarpaulins covering the scene of the case remained.