The marriage of the girl from Faridpur village was fixed with the accused, Mintu's brother Monu.
Later the girl's family snapped the engagement over a dispute, but Mintu was pressurising them for the wedding, said police.
He reached the victim's place Friday with two of his friends and tried to rape her.
When she started shouting, he set her ablaze and fled from the spot.
The girl later died at the district hospital, they said.