The man had poured fuel over himself in the first carriage of the train, a Japan Rail spokesman said.
The train was going from Tokyo to Osaka with about 1,000 people on board.
It was near Odawara city when the emergency stop button was pressed – local TV media showed pictures of the train halted with white smoke inside.
At least six others are injured, fire officials said. All trains on the Tokyo-Osaka high speed line have been stopped.
Officials have given no indication of the man’s motives but are treating the incident as a suicide.
Local media said the incident took place at 11:30 AM local time while the train was between Yokohama and Odawara.
Japan Rail officials said the train came to a stop after the emergency button was pressed and the man who set himself on fire was then discovered near the toilet stall.
The Kyodo news agency quoted transport officials as saying the driver had tried to put out the fire.
The other dead passenger, a woman, was reportedly found at the other end of the carriage.
A number of people were reported to be suffering from the effects of smoke inhalation. Television footage showed people being removed from the train by emergency services and carried across the tracks on stretchers.
Bullet trains, which have a good safety history, travel at speeds of up to 198 mph.
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