The incident occurred on Monday morning near Naihati railway station, some 40 km from state capital of Kolkata.
The woman, Purnima Das, boarded a suburban train at Naihati. As the train pulled out of the station, she flung her baby out. Shocked co-passengers pulled the chain to stop the train, and handed the woman over to police.
"The child has been hospitalised. Her condition is critical," an officer of Naihati police station said.
The woman claimed that her husband's family had been torturing her ever since she gave birth to a girl, and she wanted to rid herself of her daughter.
"Ever since I gave birth to a girl, my in-laws have been mentally and physically torturing me," Das told police after her arrest.