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.
Doctors at two-major state-run hospitals said most of the wounded were now out of danger.
Panic and chaos gripped the crowd when the bombs exploded with people running to their safety through the narrow lanes of old Dhaka, further compounding their injuries.
Security personnel cordoned-off the area while 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.
The attacks come as Shiites around the world mark the holy month of Moharram. Ashura marks the climax of the holy month of Muharram when Shias gather to mourn the martyrdom of the Prophet Mohammed's grandson Imam Hussain.
The blasts came just weeks after an Italian aid worker and a Japanese farmer were shot dead in attacks claimed by the IS, amid political instability.
Bangladesh's police chief AKM Shahidul Haque, however, downplayed IS involvement or any international links, saying the attack was likely staged to destabilise the government.
"It does not appear to be an attack carried out by Islamists... But it is a planned sabotage," Dhaka's Police Commissioner Asaduzzaman Mia said.
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