Both of the injured in the incident that took place at around 10am at Sagarpara in the city on Tuesday have been sent to hospital.
The BNP has blamed the activists of the ruling party Awami League, but the police refused to comment on the attackers.
The meeting was organised by the district wing of Jatiyatabadi Chhatra Dal at Sagarpara as part of the election campaign for Bulbul, witnesses said. BNP central leader Ruhul Quddus Talukder Dulu was present as the chief guest in the meeting.
While Dulu was delivering his speech, a group of young men arrived on the scene by motorbike, exploded three bombs near the meeting venue and fled.
BNP leaders and activists staged a protest after the meeting was foiled by the explosions.
The attack came at a time when the BNP was continuing its election campaign and trying to ward off a sense of fear among voters, said Dulu.
“Any political party should have permission from police to hold a meeting. The district wing of Chhatra Dal has never taken any permission for the meeting,” said Deputy Police Commissioner Ameer Zafar.
“We are investigating the incident to find out those responsible for it,” said Boalia Police Station chief Aman Ullah.