Sanaur Rahman, 58, a homeopathic doctor, was riding home on his motorbike alongwith Saifuzzaman, assistant professor of Bangla literature at Islami University, while they were attacked by the assailants in Kushtia town this morning.
Rahman died on the spot while Saifuzzaman has been shifted to Dhaka Medical College Hospital in critical condition, police said.
The deceased along with Saifuzzaman was going to his native village at Shishirmath to give free treatment to local people, Sahabuddin Choudhury, officer-in-charge of Kushtia Model Police Station, said.
Proloy Chisim, superintendent of police (SP) of Kushtia, said that they were also probing whether personal enmity was behind the murder.
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Both the doctor and the professor were fans of a mystical musical tradition known as Baul, which is popular in western Bangladesh.
Rahman also used to arrange musical concerts based on Baul ideology at his native village every Friday, his relative said.
There have been systematic assaults in Bangladesh in recent weeks especially targeting minorities, secular bloggers, intellectuals and foreigners.
The country's first gay magazine editor was brutally murdered along with a friend in his flat in Dhaka by Islamists two days after the professor's murder.
Less than two weeks ago, a Hindu tailor was hacked to death by machete-wielding ISIS militants in his shop in central Bangladesh.