Two cases have also been filed over the killing of 50-year-old Nikhil Chandra Joarder, who was hacked to death by three assailants who forcibly entered his house and slit his throat yesterday in central Bangladesh's Tangail district.
One of the cases was filed over the murder of Joarder and another over bombs seized from a bag left by the assailants.
"They have been detained for questioning in connection with Joardar's murder as part of the investigation," Tangail's additional superintendent of police Mohammad Aslam Khan said.
Hours after Joarder's murder, US-based SITE Intelligence Group in a statement said that the Islamic State (ISIS) group has claimed responsibility for the attack.
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ISIS' Amaq Agency reported the group's involvement in the killing of the Hindu tailor for blasphemy, it said in a tweet.
Media reports said Joarder had served three months in prison in 2012 for blasphemous comments.
"We are trying to track down the killers and called CID to probe the murder," police said.
There have been systematic assaults in Bangladesh in recent months, especially targeting minorities, secular bloggers, intellectuals and foreigners.
Last Saturday, a liberal professor was hacked to death by ISIS militants who slit his throat in Rajshahi city. Two days later, Bangladesh's first gay magazine editor was murdered along with a friend in his flat in Dhaka by Islamists.
In February, the head priest of a Hindu temple was killed in an area bordering India. It was the first attack by ISIS militants targeting the community.
In most of the cases, Islamic State or al-Qaeda in Indian Sub Continent have claimed the attacks. But the Bangladeshi government has repeatedly denies that jihadist groups were behind the spate of bloody attacks.
Prime Minister Sheikh Hasina has often denied existence of any foreign terrorist groups in the country and has attributed the deadly attacks on homegrown extremists backed by the BNP, the main opposition outside parliament, and its ally Jamaat-e-Islami.