The blast at Ramananda Chowk of Janakpur Municipality in Dhanusha district occurred while a group of Madhesi activists were staging a sit-in demanding a separate Mithila state in the new Constitution.
Three people including a woman were killed on the spot while another man succumbed to death while undergoing treatment, police said.
A lesser known group called Janatantrik Terai Mukti Morcha has claimed the responsibility for the blast.
The site of the blast has been cordoned off and a hunt has been launched to identify those involved in the blast.
The blast comes at a time when political parties in the country are busy in holding negotiations to decide contentious issues to draft the new Constitution.