With the fear of attacks expected to limit turnout and around 150 people killed in the build-up to the vote, tens of thousands of troops were deployed across the country.
But police said that more than 100 polling stations had been attacked since late Saturday into early Sunday, and officers guarding the booths had also been targeted.
The Awami League government has accused the main opposition Bangladesh Nationalist Party (BNP) of orchestrating the violence, and has kept its leader under de facto house arrest while she fumes over what is effectively a one-party contest.
Some of the worst violence was in the northern district of Bogra, which is a BNP stronghold.
"We've seen thousands of protestors attack polling booths and our personnel at a number of locations with Molotov cocktails and petrol bombs," Bogra's police chief Syed Abu Sayem told AFP.
"So far, they have set fire to 15 polling booths and attacked a police station... The situation is extremely volatile."
There were similar reports in the northern Rangpur district, where police said they had shot one person dead as protesters snatched stacks of ballot papers.
With the opposition trying to enforce a general strike as part of a strategy to wreck the polls, officials admit turnout could be worse than the previous low of 26 percent in a rigged 1996 election.
AFP correspondents in the capital Dhaka said there was no sign of queues outside the polling stations when they opened.
The outcome of the contest is not in doubt as voting is taking place in only 147 of the 300 parliamentary constituencies. Awami League candidates or allies have a clear run in the remaining 153 seats
The government says it has to hold the elections to keep in line with the constitution, but the BNP, the largest of the 21 parties who are refusing to take part, has called them a "scandalous farce".
Hasina in turn has accused BNP leader Khaleda Zia and her party of trying to hold the country hostage by staging a series of strikes and blockades, including on Sunday.
Zia has been confined to her home for the last week, with riot police manning barricades outside her Dhaka residence.
The few voters who did cast their ballots were doing so with little enthusiasm, and newspapers said Hasina should not regard the result as a mandate.
"Voting is a right, I am exercising that right, but there is no sense of celebration today," said Nurul Islam, as he voted in Mirpur, a Dhaka suburb.
With the opposition charging that the election lacks all credibility, analysts warn it will likely fuel violence in a country that has already seen its bloodiest year of political unrest since Bangladesh broke free from Pakistan in 1971.
The former East Pakistan is the world's eighth most populous nation but also one of the poorest in Asia, and more turmoil will undermine efforts to improve the lot of its population of 154 million -- third of whom live below the poverty line.
Zia says the polls cannot be fair as long as they are overseen by Hasina, calling instead for them to be organised by a neutral caretaker government.
Both women, who have a notoriously poisonous relationship, blame each others' supporters for the violence which has capped a year of political unrest.
A local rights group says more than 500 people have been killed since January 2013, a toll that includes victims of clashes between the security forces and Islamists angered by the conviction of some of their leaders for war crimes dating back to the 1971 conflict.
The main Islamist party has been banned by the courts from taking part in the election, and its leaders are either in detention or have gone into hiding.
Alarmed by the violence, the United States, European Union and Commonwealth all declined to send election observers.
The mass-selling Daily Star called it "a one-sided general election that is unlikely to end the present political crisis".
The Dhaka Tribune said "the results cannot and should not be viewed as a mandate to rule for a full term".
Bangladesh has been plagued by political instability since independence, with nearly 20 coups since 1975.