Counting will begin soon after the voting ends.
Thirteen people have been killed and thousands injured in clashes between supporters of Hasina's ruling Awami League and activists of main opposition Bangladesh Nationalist Party (BNP) of Zia in pre-poll violence. "We call them Hasina's armed cadres".
At least six candidates of the opposition National Unity Front alliance said they had pulled out alleging rigging.
Hasina and Khaleda have alternated in power for most of the last three decades and this is the first election the BNP has contested without its leader.
BNP's preparations have been hamstrung by the February jailing of its chairman, former prime minister Khaleda Zia, on what the party called trumped-up corruption charges.
The BNP-led opposition alliance yesterday accused Hasina's party of using stuffed ballot boxes and other illegal means to fix the result, which is to be announced today.
The opposition fielded candidates for all 299 parliamentary seats that were contested.
Voters will have to turn off their mobile phones before entering the centres. "Especially women voters are being forced to vote for the boat", Alal said, referring to the Awami League symbol.
"We have asked our officials to deal with them", K.M. Nurul Huda, Bangladesh's chief election commissioner, said as he cast his vote in Dhaka, the capital.
In a 300-member Bangladesh parliament, a party needs 151 seats to form the government.
Walking with a cane, Mr Hossain cast his vote near his home in Dhaka, saying that he was receiving complaints about vote-tampering and intimidation from various parts of the country.
Internet services were slowed across the country, with 3G and 4G services suspended for several hours, a Bangladesh Telecommunication Regulatory Commission official said yesterday. One independent television news channel complained that its broadcasts were blocked.
"They told me that "voting is going on nicely, you don't need to go inside". But its leaders, candidates such as Khan, and workers say they are facing violent attacks and intimidation, including shootings and arrests, that have stunted their ability to campaign.
There are some 104 million registered voters, according to Bangladesh's election commission.
A middle-aged businessman who declined to be named said: "I am here to vote, but my family says, 'what's the point?' The ruling party will come back in power in any case". "We hope that by that night we will get the result of all constituencies, if nothing untoward happens", he added.
The opposition said the unrest was stirred up to deter voters, and presiding officers reported a low turnout across the country.
The election campaign was marred by violence between supporters of Hasina's Awami League and Zia's BNP.
While rights groups sound the alarms about the erosion of Bangladesh's democracy, Ms Hasina has promoted a different narrative, highlighting an ambitious economic agenda that has propelled Bangladesh past larger neighbours Pakistan and India by some development measures.
Hasina's party was leading in 114 seats while the BNP was ahead in two, according to TV channels.
The sample size of the survey was 2,249 and the respondents were drawn from the constituencies of 51 parliamentary seats on December 9-16, said Forrest E. Cookson, an American consultant who presented the findings at a news conference. The Awami League's landslide victory was met with violence that left at least 22 people dead.
Sixteen global human rights groups released a joint statement Saturday saying the crackdown "compromises the integrity" of the vote.
The same day, the new USA ambassador to Bangladesh said he had met with the chief election commissioner and the rest of the commission because the United States was concerned "by the high level of campaign violence over the last two weeks".
Her government was criticised earlier this year for its heavy handling of weeks of massive student protests over the abolition of job quotas and poor safety standards on Bangladesh's risky roads.
But since her last victory, civil society and rights groups have accused Hasina's government of silencing dissent and muzzling the press.