The suspect, 36, allegedly told police he became angry when he saw women who "looked happy" and wanted to kill them, according to local media reports.
One victim, a female student, is said to be seriously injured, while the others suffered less severe injuries.
Violent crime is rare in Japan and tight security measures are in place in Tokyo, which is hosting the Olympics.
The man attacked passengers on a train near Seijogakuen station at about 20:40 (11:40 BST) on Friday.
The train was brought to an emergency stop by the driver after they heard noises coming from inside the carriages.
According to investigators, the suspect jumped onto the tracks and fled. Train crew guided the passengers along the tracks to the nearest station.
One witness, who was on the train, told NHK news that people suddenly started running towards him, fleeing from one car to another.
The suspect later walked into a convenience store and told staff that he was "the suspect in the incident reported by news media" and was tired of fleeing.
Tokyo Metropolitan Police confirmed early on Saturday they had seized a man in his 30s but did not confirm reports of his arrest or give any further details.
Nine out of the 10 injured were taken to hospital while the other walked away from the scene.
Despite Japan being one of the safest countries in the world, there have been a number of knife attacks in recent years.
In 2019, a man attacked a group of schoolchildren waiting for a bus in Kawasaki. Two people were killed and at least 18 were injured.