The man, identified as Upendra Kumar, pulled the hands of the 13-year-old girl and jumped out of the passenger train last night, Superintendent of Police Varun Kumar Sinha said.
The girl died on the spot, while Kumar sustained injuries, the SP said.
Kumar, said to be of dubious background, was not known to the victim, Sinha said.
The girl was going with her parents to Samastipur district from Simariaghat in neighbouring Begusarai district, the SP said.
The girl's father Tapeshwar Verma raised an alarm upon which the train stopped and the GRP personnel nabbed the accused, he said.
An investigation was going on in the matter, Sinha said, adding the victim's body has been sent for post-mortem.