"We have been informed that there was a passenger in a car on the train who covered him or herself with oil and set it on fire," a spokesman for operator JR Central told AFP.
The Yomiuri Shimbun daily said a blast was heard from a toilet stall, with the emergency bell pressed soon afterwards, which brought the train to a halt.
Media reported that the driver of the train found the still-burning body of a man after the emergency stop.
"We received information indicating that a fire broke out near a toilet and two people were in cardiopulmonary arrest," a spokesman for Odawara Fire Department said.
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"Other passengers were also injured," he said, adding that two were in a serious condition.
NHK reported the two people feared dead were found on the floor of the first car, but at opposite ends of the carriage.
TV Asahi said the second person found lying on the floor was a woman who had been overcome by smoke.
The fire erupted at around 11:30 am (local time) when the train was about 70 kilometres (45 miles) from the capital.
Television pictures showed all the doors on the stationary train were open and passengers were being carried out on stretchers.
Prime Minister Shinzo Abe set up a task force to respond to the incident, TV networks said.
Japan's ultra-efficient shinkansen train network connects cities along the length and breadth of the country.
The first service connecting Tokyo and the western commercial hub of Osaka, some 500 kilometres away, began in 1964, as Japan prepared to host the Olympic Games.
An average of more than 400,000 passengers use the service daily, travelling at speeds of up to 285 kilometres per hour, with around 300 trains running in both directions each day.
When the system marked its 50th anniversary last year, the Tokyo-Osaka line had carried a total of 5.6 billion passengers, with trains travelling a cumulative 2 billion kilometres, enough to circle the globe 50,000 times.