The victim, who was travelling alone from Nainpur station, was being harassed by the accused since they boarded the train last night, they said.
Police said the girl alighted from the train at Balaghat railway station at around 3 AM and decided to wait as none of her relatives came to receive her.
Seeing her alone, the youths forcibly took her to a nearby lodge and raped her before fleeing.
Based on the victim's complaint, police arrested Rahul Tiwari (21), Nilesh (20) and Rahul Rodan (20).