"It was an incident of suicide bombing. The suicide attacker targeted our camp," Rapid Action Battalion (RAB) spokesman Commander Mufty Mahmud said.
Authorities have issued an alert for all international and domestic airports and prisons in the country and ordered to step up security.
"It is not a red alert, but we have received orders for more vigilance. We are always alert. We have been told to intensify our security because of that incident," said Superintendent Jahangir Kabir of Dhaka Central Jail.
It is the first attack ISIS has claimed in Bangladesh this year and 27th since September 2015.
Over 70,000 inmates are lodged at 68 jails in the country.
The area where the incident took place was earmarked for constructing the headquarters of the force.
The blast wounded two RAB men who were being treated at the nearby Combined Military Hospital in Dhaka Cantonment.
The officer said the attack appeared to be an act of any militant outfit, but it was not clear immediately which of the Islamist outfits staged it.
Witnesses said the youth exploded a powerful bomb as several RAB men gathered at a common bathing place at the camp, killing himself instantly and seriously wounding two members of the elite force which draws personnel from army, police, navy and air force.
Residents in the neighbourhood said the bomber, aged around 25 years, apparently sneaked into the complex after scaling the wall.
Bangladesh has witnessed a nationwide anti-Islamist crackdown since last week while police said they arrested over 80 militants.
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