The bomb, carried by a man on foot, exploded near a police checkpoint monitoring vehicles heading to Hazrat Shahjahal International Airport.
"The bomb carrier himself was killed," a Dhaka police spokesman, Yusuf Ali, told AFP.
Ali did not say whether the attack had specifically targeted the checkpoint.
The suspected attack was the third since last Friday, when a suicide bomber blew himself up at a camp for the country's elite security force near the airport.
The attacker was killed and two members of the Rapid Action Battalion, tasked with combating Islamist militancy, were injured.
The ISIS group claimed the attack, saying "a caliphate soldier in Bangladesh carried out a martyrdom operation with an explosive belt".
The Bangladeshi government deny the presence of ISIS in the country and reject the terrorists' claim.
The Bangladeshi government argues a new faction of homegrown extremist group Jamayetul Mujahideen Bangladesh (JMB) was behind that and other attacks.
Last Saturday a man on a motorbike tried to cross a RAB security roadblock in Dhaka carrying a bag with improvised explosive devices.
Bangladesh police shot the suspected militant dead.
The latest incident came as police in the northeastern city of Sylhet cordoned off a five-storey building early Friday morning where suspected extremists were holed up.
Police have also been carrying out a series of raids in the southern Chittagong region and say they killed four suspected militants when they stormed an extremist hideout last Thursday.