Opposition parties are boycotting the election after the government of Prime Minister Sheikh Hasina refused to install a caretaker government to oversee the election, the BBC reported Saturday.
Khaleda Zia, leader of the opposition BNP party, called the election a "scandalous farce."
A former prime minister, Zia has charged the government is holding her under house arrest, Voice of America reported.
All elections have been held under a caretaker government since 1991 to ensure voting is fair. Hasina's Awami League abolished the caretaker system four years ago, saying it was no longer needed.
The United States, the European Union and the Commonwealth have all refused to send election monitors.
Despite the attacks on the polling stations, a government administrator in the Chittagong region said no polls would be canceled.
At least 100 people have been killed in violence in the weeks leading up to the elections. At least 12 were hurt when a firebomb was thrown into a train in the northwest town of Natore, police said.
Some 50,000 troops are reportedly deployed around the country for the election.