The explosions took place when people were gathered to attend a religious ceremony known as "Rushmela at Dinajpur district in northern Bangladesh, said a police official, reported Reuters.
Priests in Bangladesh were recently threatened not to organise any religious congregation. Five persons have bene detained for interrogation in connection with the explosions.
The attack follows the shooting and wounding of an Italian doctor working in the same region last month, and the earlier murders of an Italian and a Japanese citizen in separate attacks claimed by Islamic State.
Bomb attacks on Hindu religious gatherings are rare in Muslim-majority Bangladesh.
Human rights groups and Hindu leaders in Bangladesh have been demanding more security for minorities amid regular reports of attack on them in several parts of the country.
Iidols of goddess Durga were vandalised by unidentified miscreants in southern Bangladesh during Durga puja.
It has been a long period of over 40 years since independence Hindus in Bangladesh remain vulnerable to attacks by anti-liberation forces.