The priest was killed and the devotee wounded Sunday in the latest attack on minority religious figures in the predominantly Muslim nation.
Two of those arrested are activists in the outlawed Islamist organization Jamaatul Mujahedin Bangladesh, Police Inspector Muhammad Babul Akhter said. The other is a member of Jamaat-e-Islami, the country's largest Islamic political party.
They have been charged with murder and possession of weapons.
Despite media reports
of claims of responsibility by ISIS
, the official said that police have not found any evidence of a connection with the extremist group so far.
Two people attacked the 50-year-old Hindu priest in a temple in Bangladesh's northern district of Panchagarh on Sunday morning, Panchagarh district police Chief Giasuddin Ahmed said.
The attackers approached on a motorcycle, hurling grenades and firing bullets at the temple, before slitting the priest's throat and fleeing, Ahmed said. A devotee at the temple was also wounded in the assault.
Police had ramped up security in Hindu temples and centers in the district after receiving anonymous threats, Ahmed said.
Islamist group targets minorities
The killing is the latest attack on minority religious figures and institutions in the country in recent months.
In October, a Christian pastor was attacked in northwest Bangladesh, and the following month, an Italian Catholic priest was attacked in the north. Both men survived.
Also in November, a Shiite mosque was attacked in Bogra
, northern Bangladesh, leaving one dead and three wounded. ISIS claimed responsibility for that attack.
Monirul Islam, the joint commissioner of the Bangladesh Police, said that Jamaatul Mujahedin Bangladesh was behind previous attacks on religious minority leaders and institutions and that the hardline organization was the main suspect in the latest killing.
"This group is responsible for most of the attacks on Shiite mosques, Hindu temples, churches and religious leaders across Bangladesh since October," Islam said.
The JMB is one of six banned Islamist groups in the country and has been blamed for bombing campaigns
and other terrorist acts.
Nearly 90% of Bangladesh's estimated 169 million people are Muslim, with a Hindu minority of about 10%, and other minorities, such as Christians and Buddhists, making up less than 1%, according to the CIA World Factbook