Wielding a survival knife, he took five hostages and was demanding the Noda cabinet step down, as well as asking to speak with journalists, major media said.
The man was also asking for 10 days worth of food and water as well as a megaphone, the Asahi Shimbun said.
Noda last week called an election for December 16. He is expected to lose, with polls suggesting the main opposition Liberal Democratic Party will be the biggest party.
The hostages were four bank staff and one customer, major media said.
Television footage showed the area around the bank sealed off and guarded by police officers.