Bangladesh has suffered a wave of Islamist militant violence in recent months, including a series of bomb attacks on mosques and Hindu temples.
Some of the attacks have been claimed by Islamic State, which has also said it is behind the killings of a Japanese citizen, an Italian aid worker and a policeman.
In Sunday's attack, five or six motorcycle-borne attackers cut the throat of the priest, Jogeshwar Roy, 55, as he was organising prayers at the Deviganj temple near Panchagar, 494 km (308 miles) north of the capital, Dhaka, police said.
"We suspect that they might be members of the banned Islamist militant group Jamaatul Mujahedeen Bangladesh (JMB)," police official Humayun Kabir told Reuters.
The Islamist militant group could not be reached for comment. No group has so far claimed responsibility.
The motive for the killing was probably to create an unstable situation in the country and ultimately establish a caliphate, Kabir, the deputy director general of police in the area, added.
One devotee who tried to stop the priest's attackers was shot in the leg before the group fled, he said. Police have not yet made any arrests.
The government denies that Islamic State has a presence in the country of 160 million people. Police have blamed earlier attacks on home-grown Islamist militants.
