Arjun Biswas, 42, headmaster of Monas Government Primary School, was attacked with sharp edged weapons, they said.
The incident took place at Manash Village in Netrokona district, about 165 kms from here, this morning when he was on his way to the school from his home, according to local media reports.
Police said that Biswas died on the spot.
He might have been killed following a conflict between the school's managing committee members, police suspects after prima facie investigations.