The priest, Ananda Gopal Ganguly, was on his way to temple when the assailants attacked him in a field in a secluded part of a village in the country's Jhenaidah district, Altaf Hossain, a police superintendent, told CNN.
He said police have never received complaints about threats to the Hindu community in the village.
"We believe the attackers came from outside the village," Hossain said.
An investigation is underway.
Deadly hackings have become increasingly common in Bangladesh.
Three men shot and stabbed her to death while she was taking her son to catch a school bus.
Crackdown on militants kills 3
Also Tuesday, police killed three militants from the group Jamaatul Mujahideen Bangladesh, police official Mashruqur Rahman Khaled told CNN.
Two were killed in Dhaka, the capital, and another in the northwest Rajshahi district.
Authorities say the Dhaka militants, killed after a shootout with police, were involved in planning terrorist activities in northern Bangladesh, including bombing a Shiite mosque and killing Rezaul Karim Siddique, 58, a university professor.
They were targeted as part of an operation to crack down on militants, Khaled said.