Mir Sanwar Rahman, known for offering villagers free homeopathic medicines, was hacked to death early on Friday in Kushia district.
No group has said they carried out the attack.
There has been a spate of murders of religious minorities, secular activists and academics in Bangladesh recently.
Mr Rahman and tutor Mohammad Saifuzzaman were ambushed as they travelled on a motorbike in their village, police say.
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Police official Proloy Kishim told the BBC Bengali service the two men had both been struck on the head and neck by machetes.
Mr Saifuzzaman was being brought to the capital, Dhaka, as his injuries were too grave for the local hospital to treat, the BBC's Akbar Hossein in Dhaka reports.
The motive for the attack is unclear. However, police chief Mohammad Sahabuddin Chowdhury told AFP news agency: "We suspect Islamist militants are behind the attack."
More than 20 people have been killed in attacks by suspected Islamists in the last three years.
An elderly Buddhist monk was hacked to death on Saturday while a Hindu priest, two prominent gay activists, a law student and a university professor were also murdered in recent months.
The killings have been blamed on various hardline groups, including so-called Islamic State (IS) and Ansar al-Islam, a Bangladeshi militant group affiliated to al-Qaeda.
The government has denied that IS is present in the country. Instead, it has blamed opposition parties and local Islamist groups, such as Ansarullah Bangla Team and Harkatul Jihad.
The opposition have denied any involvement and say the government's accusations against them have hampered a credible investigation.
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