The unidentified gunmen entered the Mosjid Al Hussain in Horipur area and opened fire indiscriminately on the worshippers soon after the evening prayers, police said.
In the firing, the mosque's 70-year-old muezzin, Moyazzem Hossain, died while three others were injured and had been admitted in a hospital, the Daily Star reported. No one immediately claimed responsibility for the attack.
The incident comes a month after a grenade attack on a Shia shrine in the capital Dhaka killed one and hurt 80. Bangladesh has seen several violent incidents in recent months, including attacks on foreigners and secular bloggers carried out by Islamist radical groups.
Shias are a minority in Sunni-majority Bangladesh, a Muslim-majority nation of 160 million people.