The country's main port, Chittagong, was reported to be badly hit and transport elsewhere was disrupted.
More than 200 people were injured in clashes with police and in a series of bomb blasts preceding the strike.
The strike was called by the opposition to try to force Prime Minister Sheikh Hasina to call early elections.
General elections are due in July and the prime minister's Awami League party has vowed to serve out its full term.
The strike shut down businesses and schools with traffic in the capital, Dhaka, coming to a standstill.
The country's main port, Chittagong, was reported to be badly hit and transport elsewhere was disrupted.
Sunday is a working day in Bangladesh, which is a Muslim majority country.
Government and opposition supporters clashed in the country's major cities - Dhaka, Rajshahi and Chittagong.
Opposition threat
Last month, the four-party opposition alliance - which includes opposition leader Begum Khaleda Zia's Bangladesh National Party - gave Sheikh Hasina an ultimatum to step down or face a protest.
The prime minister had earlier announced she would step down after 17 April and hand over power to a caretaker administration, but has since changed her mind.
"We have changed our plan to hold early polls after the opposition issued the ultimatum," she told a rally of her supporters in Dhaka on Saturday.
"We can't bow to its illogical threat," she said.
Under the country's constitution, the prime minister has to hand over power to an interim administration ahead of elections.
But Sheikh Hasina's five-year term does not end before mid-July.
The stand-off has led to fears of more violence before the elections and has also hurt the country's economy.
Business leaders say the strikes have cost Bangladesh billions of dollars in lost production and exports.