He is critically ill in hospital.
The assault, in the town of Madaripur, is the latest in a series of recent attacks on religious minorities, secular writers and academics.
Last week, Bangladesh's prime minister vowed to bring an end to the violence, and police launched an operation against Islamists.
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Ripon Charkavarti was attacked with machete knives as he opened the door at his home.
Police said they are questioning one of the three suspects caught by local people while trying to escape.
Earlier attacks have been widely attributed to Islamist extremists and are causing growing concern.
In many cases, the Islamic State group or al-Qaeda say they carried out the attacks but the government denies the group is active in the country, our correspondent in Dhaka, Waliur Rahman, says.
The Prime Minister of Bangladesh, Sheikh Hasina, has said her government will do whatever it takes to stop the attacks.
"Where will the criminals hide? Each and every killer will be brought to book," she told a meeting of her governing Awami League party on Saturday.
Police launched a campaign last Friday, and have arrested thousands of people.
However, critics say many ordinary criminals were among those held.
More than 40 people, including secular bloggers, academics, gay rights activists and members of religious minorities, have been killed in attacks blamed on Islamist militants in Bangladesh since February 2013.
Last Friday, a Hindu monastery worker was hacked to death in Pabna district.
Over the past two weeks, a Hindu priest, a Christian grocer and the wife of an anti-terror police officer were all killed in attacks by suspected Islamist militants.
A Hindu college teacher in Bangladesh has been attacked on his doorstep by three men armed with knives, according to local police.