Video footage shows passengers running through carriages away from flames and clambering out of train windows.
The incident happened at around 20:00 local time (11:00 GMT) near Kokuryo station, in the city's western suburbs.
Police say a man in his 20s was arrested at the scene. Local reports suggest he was in a Halloween costume.
Eyewitness reports and footage appears to show a suspect in a bright purple and green suit, similar to the Joker character from the Batman comics.
"I thought it was a Halloween stunt," one witness told the Yomiuri newspaper about the attack. "Then, I saw a man walking this way, slowly waving a long knife."
Eyewitnesses say the suspect sprayed a clear liquid around the carriage before setting it alight.
The AP news agency, citing the Tokyo Fire Department, said three people were seriously injured. Local media reports an elderly man was unconscious after being stabbed in the attack.
Video from the scene shows passengers running from the attacker, stumbling through a connecting door between carriages and climbing through the train's windows after it made an emergency stop.
Shunsuke Kimura, who filmed one of the videos, told the national NHK broadcaster that the scene was "horrifying".
"Train doors were closed and we had no idea what was happening, and we jumped from the windows," he said.
Other footage from the scene appears to show the suspect being taken into custody by police.
Violent crime is rare in Japan but there have been a number of high-profile knife attacks in recent years.
Ten people were injured by a knife wielding man on another Tokyo commuter train in August.
A man attacked a group of schoolchildren waiting for a bus in Kawasaki in 2019 - killing two and injuring at least 18 others.