The bombing comes just weeks after an Italian aid worker and a Japanese farmer were shot dead in attacks claimed by the Islamic State.
Police and witnesses said three bombs were hurled at the procession joined by more than 20,000 people at around 1:30 AM at Huseni Dalan, an important 17th century centre of learning for the Shia community.
Hours after the attack, the US-based Site Intelligence Group that monitors militant threats reported that the Islamic State claimed the responsibility for the bombing on the Shiite shrine.
However, Bangladesh police earlier suspected the blasts were carried out by a domestic group to create instability.
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The Islamic State claim came even as home minister Asaduzzaman Khan Kamal ruled out possibilities of Islamist links to the attack saying, "this is not a militant attack, rather it is a planned and destructive attack aiming only to destabilise the situation of the country."
"Until now we have found no IS link or any (Islamist) militant groups involvement in the Hussaini Dalan blasts," a police spokesman told PTI.
Defying the security threat, Shiites went ahead with their scheduled processions to mark Ashura, the 10th day of the Islamic month of Muharram, marking martyrdom of Imam Hussain, grandson of Prophet Mohammad.
"One of the bombs directly hit a 12-year-old boy and he died instantly," a police official said.
Panic and chaos gripped the crowd when the bombs exploded with people running for their safety through the narrow lanes of old Dhaka, further compounding their injuries.
Security personnel cordoned-off the area and the elite anti-crime Rapid Action Battalion (RAB) and armed police escorted people out of the blast site.
"In Bangladesh we have been observing the holy Ashura for centuries, but this is the first time we came under such a gruesome and cowardly attack," a Shia leader told reporters hours after the attack.