ISIS released a statement saying its "soldiers of the caliphate" are responsible for the priest's death.
"God willing, the knives of Mujahedeen will continue until we cleanse Bangladesh from the wrath of polytheism," the statement said.
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.
Ganguly's killing comes days after Mahmuda Khanam Mitu, the wife of a prominent anti-terror police officer, was killed in Chittagong.
Three men shot and stabbed her to death while she was taking her son to catch a school bus.
Last month, ISIS claimed
responsibility for hacking a doctor to death; a man was arrested
in the killing of two lesbian, gay, bisexual and transgender activists; a Buddhist monk had his throat slit
; a Sufi spiritual leader's body was found in a mango orchard
; and three people were detained
in relation to the hacking death of a Hindu tailor.
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.