The train, carrying about 1,000 passengers, made an emergency stop on its way from Tokyo to the western city of Osaka after smoke started to fill at least one carriage, fire department officials said.
A fire department official confirmed that one man was dead. Kyodo news agency, quoting a witness, identified him as the man who had covered himself with oil and set fire to himself.
There was no immediate indication of any possible motive for the man's actions.
A female passenger also died, NHK public TV said, while at least one more was in serious condition and several others suffered less serious injuries, fire department officials said.
Most passengers went to other carriages after smoke began to fill the car, reports said.
An official at JR Tokai (Central Japan Railway Company), which operates the train, said at least one person was found at the entrance of a carriage covered in flammable liquid.
Footage on TBS television showed a train carriage filled with smoke and passengers evacuating with handkerchiefs pressed to their faces. One clutched a baby to their chest.
Smoke inside the Japan bullet train after a passenger set himself on fire.
The JR Tokai official said the train stopped after the emergency button was pushed and the passenger was then discovered. No further details were immediately available.
Japan's superfast Shinkansen trains are known for their speed and safety.
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