The Islamic State (IS) has claimed the responsibility for the attack on the police checkpoint in Ashulia industrial area on the outskirts of Dhaka.
The attack led to the death of police constable Mukul Hossain and left another constable critically injured.
The US-based SITE Intelligence Group, which tracks online activity of White supremacist and jihadi organisations, confirmed the report.
However, the reason for the attack is still unknown.
An Assistant Sub-Inspector of Darus Salam Police Station was stabbed to death last month by a youth at a checkpoint in the capital's Gabtoli area.
These incidents are coming to the fore at a time when Bangladesh is reeling with the fear of the rise of Islamist violence, after four atheist bloggers were murdered this year.
However, the Bangladeshi Government has repeatedly asserted the non-existence of IS in the country.