Hasina is confident of a third straight term in a face-off against an opposition whose leader is in jail charged with corruption.
Polling is currently underway at more than 40,000 polling stations in 299 constituencies.
Mobile internet services were blocked and security has been beefed up in the wake of polls.
According to sources, at least five people were killed and more than 30 injured in poll-related violence.
Around 104.2 million people including millions of young new voters are registered to vote in the first fully competitive general election in a decade.