The attack reportedly took place in a popular shopping area.
The perpetrator was arrested, the news agency said.
Traffic on the Yamanote Line of the Tokyo railway was reportedly suspended due to the incident.
Later in the day, another Japanese media outlet reported that the attack had taken place on a train and that the perpetrator was a woman.
A police source told media that law enforcement officers had received a tip that "a woman was brandishing a knife" in a car of the train that stopped at the Akihabara station.
Kyodo News said that the woman was arrested on suspicion of attempted murder. Her exact age is unknown, but she reportedly appears to be between 20 and 30 years old.