The 13 were detained at Teliamura railway station, about 45 km from here, yesterday, they said.
The Bangladeshis, all residents of Habiganj in the neighbouring country, entered India via Khowai district and were to board a train to go to Delhi and Ajmer Sarif in Rajasthan, police said.
During interrogation, a woman told police she was going to her daughter's house in Delhi and others were going to Ajmer Sharif, they said.