Police and witnesses said the bomb exploded on Thursday at a rally of the main opposition Awami League at Laskarpur, 250km from capital Dhaka.
About 50 other people were wounded.
An Awami League spokesman said former Finance Minister Shah Abu Mohammad Shamsul Kibria, 70, was among the dead.
Others who died in the blast included a nephew of Kibria and two party workers.
After the blast, protesting Awami workers and supporters went on a rampage, attacking and damaging dozens of vehicles and shops, witnesses said.
Kibria who had been sitting on the dais at the rally when the bomb went off, died in a Dhaka hospital around midnight.
Hospital doctors confirmed his death to reporters, and said another person taken to the hospital was fighting for his life.
The Awami League is the major
opposition party in Bangladesh
"Kibria is dead," the party spokesman said, without giving details.
In protest, the Awami League has called for a nationwide general strike on Saturday following countrywide protests on Friday.
Police were investigating whether the bomb had been planted before the rally or had been thrown.
The Awami League quickly blamed the government.
"The blast came in the wake of an unending conspiracy by the government to eliminate democratic forces, especially its opponents," said Sabir Hossain Chowdhury, political secretary to Awami League leader Shaikh Hasina, a former prime minister.
Hasina narrowly escaped injury in August when at least three grenades exploded at a rally she was addressing in Dhaka.
In May, British High Commissioner Anwar Choudhury was wounded in a bomb blast at the shrine of a Muslim saint. Three people were killed in the blast.
In her recent public speeches, Prime Minister Begum Khaleda Zia has accused the opposition of trying to create anarchy in the country through shutdowns and lawlessness, and vowed her government would resist such attempts.