The priest was a prominent member of Bangladesh's Hindu community, which makes up nearly 10 percent of the South Asian country's population of 168 million.
JMB was blamed for the murders of minorities, secular writers, publishers and foreigners between 2013 and 2016.
Among them was a savage attack at a Dhaka cafe in 2016 that killed 22 people, mostly foreigners.
Seven Islamist extremists were sentenced to death in November over the assault that was claimed by the IS.
Bangladesh security forces launched a nationwide crackdown after the cafe siege, killing more than 100 members of the JMB including its top leaders, and arresting hundreds of suspected militants.