Sunil Gomes, 65, was found dead inside his grocery shop at around midday in northwestern Notore district, police superintendent Shyamal Mukherjee told PTI over the phone.
The assailants fled the scene immediately after hacking to death Gomes inside his shop at the commercial hub near a church at Banpara village at the outskirts of the district town, he said.
"We are yet to know the details of the incident but our policemen are gathering information about the murder," Mukherjee said.
The motive behind Gomes' murder was now known immediately, the police said.
Meanwhile, in a separate incident, the wife of a top Bangladeshi police officer who carried out several raids against militants was stabbed and shot dead by three bike- borne assailants in front of her minor son in the port city of Chittagong.
Mahmuda Aktar, 33, was targeted by the gunmen at around 6:45 am (local time) while she was on her way to drop her six- year-old first-grader son to a nearby bus stop for school in Chittagong.
The police suspect religious extremists were behind her murder, Home Minister Asaduzzaman Khan Kamal said. She was the wife of Superintendent of Police Babul Aktar, now posted at the police headquarters in Dhaka.
Babul has led several raids on militant hideouts and investigated several terror-related cases as the additional deputy commissioner with the detective branch in Chittagong.
Babul, who was promoted in April, played a key role in nabbing top militants and busting their hideouts in the southern coastal district. It was his investigations which led to the busting of a hideout of banned outfit Jama'atul Mujahideen Bangladesh and arrest of its military wing chief Mohamed Javed in October last year.
"Since Babul Aktar was in counter-terrorism, we suspect that militants are behind the murder of his wife," Detective Branch Deputy Commissioner Moktar Ahmed was quoted by bdnews24 as saying.
Quoting witnesses, Chittagong metro police's Deputy Commissioner Paritosh Ghose said that three bike-borne attackers ambushed Mahmuda in front of her minor son. The boy said the attackers first took him away and then one of them stabbed his mother with a knife before shooting her.
The police said that Mahmuda was shot in the head. "We found three live ammunition and a used casing on the spot. The bullet hit her on the left side of the head," said Police Bureau of Investigation's Additional Superintendent Bashir Ahmed. She is survived by a four-year-old daughter.
There have been systematic assaults in Bangladesh in recent months specially targeting minorities, secular bloggers, intellectuals and foreigners.
In the recent attacks, a liberal professor was brutally hacked to death in April by machete-wielding ISIS militants who slit his throat near his home in Rajshahi city. There have been systematic assaults in Bangladesh in recent weeks especially targeting minorities, secular bloggers, intellectuals and foreigners.
In the recent attacks, a liberal professor was brutally hacked to death in April by machete-wielding Islamic State militants who slit his throat near his home in Rajshahi city.
Two days later, Bangladesh's first gay magazine editor was brutally murdered along with a friend in his flat in Dhaka by Islamists.
On April 30, a Hindu tailor was also hacked to death by machete-wielding ISIS militants in his shop in central Bangladesh.
The IS and Al Qaeda in IndianPeninsula have claimed responsibility for some of the attacks although the government denies their presence in Bangladesh.