At least two attackers stopped Hossain Ali in the town of Kurigram on Tuesday morning before lunging at his neck with sharp weapons, police say.
The 68-year-old, who converted from Islam to Christianity in 1999, died on the spot and officers are unsure whether Islamists are responsible or whether there was a different motive.
They are yet to identify Mr Ali's attackers.
Bangladesh is Muslim-majority nation and militants purporting to be from Islamic State (IS) have in recent months claimed responsibility for a number of attacks on converts and religious minorities, including Christians.
According to the AFP news agency, Prime Minister Sheikh Hasina's government (Hasina pictured above) denies IS is operating in Bangladesh.
The government claims the banned home-grown militant group Jamayetul Mujahideen Bangladesh is responsible for the rise in violence.