The 22-year-old assailant, named by authorities as Ichiro Kojima, was arrested late Saturday after police stormed the train when it made a stop at Odawara station west of Tokyo.
News reports said two women who appeared to be in their twenties were also wounded but their injuries were not life-threatening. The prefectural police will investigate details, including his motive. At some point, Kojima then overpowered and stabbed Umeda, who tried to stop him.
Passenger killed in knife attack on Japan bullet train
Public broadcaster NHK reported that the suspect told police he felt "frustrated and wanted to kill someone".
Witnesses said passengers fled in panic, some of them in tears.
A passenger eventually called the police, saying there was a knife-wielding person on board and that people were bleeding.More news: Scotland beat England for the first time in a one-day worldwide
According to JR Central, an average of 446,000 passengers used Tokaido Shinkansen trains each day in fiscal 2015.
After being hospitalized for an undisclosed mental illness, he started working for a machinery maintenance firm in April 2015 but quit in February the following year. The train was bound for the western city of Osaka.
He talked about suicidal thoughts before running away, she said.More news: Natural disaster and ash eruption hit Kilauea volcano
The attack occured on Saturday night, when the train was travelling with nearly 900 passengers onboard west in Kanagawa Prefecture, south Tokyo. The train was carrying more than 800 passengers at the time of the incident.More news: Net neutrality rollback: FCC chairman Ajit Pai responds to critics