The counterterrorism unit detained the three on Tuesday afternoon from Zigatala's Moneshwar Road.
"The three have been brought in for questioning," Counterterrorism Unit Deputy Commissioner Saiful Islam told bdnews24.com.
Akayed's wife Jannatul Ferdous and their six-month-old child live with her parents at a home on Moneshwar Road.
Akayed, 27, who hails from Chittagong, has lived in the US for seven years. US police officials say he started as a cab driver and then became an electrician at a real estate company after 2015.
New York City police detained Akayed after he had injured himself after detonating a pipe bomb at the crowded Port Authority Bus Terminal in Manhattan. He was later admitted to hospital.
US police officials say the bomb was tied to his body.
They claim Akayed had been inspired by Islamic State propaganda.
Bangladesh police began searching for Akayed's family after his identity was confirmed.
An official from the counterterrorism unit said they found the address of Akayed's in-laws on Tuesday afternoon.
Akayed's father-in-law Zulfikar Haider, mother-in-law Mahfuza Akhtar and their children rented the house.
The Bangladesh embassy in Washington DC reiterated Prime Minister Sheikh Hasina government's 'zero tolerance' policy against terrorism.
"A terrorist is a terrorist irrespective of his or her ethnicity or religion, and must be brought to justice," the embassy said in a statement.
"Government of Bangladesh is committed to its declared policy of 'Zero Tolerance' against terrorism, and condemns terrorism and violent extremism in all forms or manifestations anywhere in the world, including Monday morning's incident in New York City."
Akayed is said to be in serious condition at Bellevue Hospital Center.
The local media have published a photo of the bearded suspect lying on the ground with burn injuries on his belly.
New York Post reported quoting sources in the police that the suspect had wires attached to him and a 5-inch metal pipe bomb and battery pack strapped to his midsection.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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Doraiah Chowdary Vundavally is a Software engineer at VTech . He is the news editor of SocialNews.XYZ and Freelance writer-contributes Telugu and English Columns on Films, Politics, and Gossips. He is the primary contributor for South Cinema Section of SocialNews.XYZ. His mission is to help to develop SocialNews.XYZ into a News website that has no bias or judgement towards any.