Dinesh Trivedi quit after his Trinamul Congress party, a key ally of the government, after he refused the party’s demand to roll back the rise.
Mr Roy announced modest passenger fare rises last week, the first in nearly a decade on the huge state-run system.
The party had nominated Mr Roy, another party MP, for the job.
India’s state-run railway operates 7,000 passenger trains and carries some 13 million passengers daily.
Hours before Mr Roy was sworn in, a train crashed into a vehicle at an unmanned level crossing in Uttar Pradesh state, killing 15 people travelling in the vehicle.
Correspondents say Mr Roy is expected to roll back some of the fare increases, a key demand of his party leader, Mamata Banerjee.
Mr Trivedi raised the fares in last Wednesday’s railway budget by a maximum of 30 paisa ($0.006; £0.0038) per km, saying the network was passing through a “difficult phase”.
Mr Trivedi had said he had been advised to impose a big fare increase as there had been none in nearly a decade, but had opted for a modest rise instead, out of “concern for the common man”.
Railways officials say the jump in fuel prices over the last eight years has badly affected their bottom line.
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