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.
They said it was believed to be the first attack on the Shias in the Sunni-dominated Bangladesh, which has witnessed an increase in violence this year claimed by the Islamic State (IS) terrorist group.
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.
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."
"Local and international gangs are involved in a conspiracy aiming to destablise the country and create panic among people," he told reporters while visiting a state-run hospital to meet the Shiites wounded in the attack.
"Until now we have found no IS link or any (Islamist) militant groups involvement in the Hussaini Dalan blasts," a police spokesman said.

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