The protester was killed in the northern town of Chirirbandar ahead of Tuesday's shutdown of businesses and schools called for by the Jamaat-e-Islami Party.
A special court is trying senior leaders of Jamaat-e-Islami for allegedly carrying out atrocities during the 1971 independence war, the BBC reported. Other party leaders say the charges are politically motivated and have called on workers to stop work and close shops in protest, the BBC said.
Schools and businesses in many parts of the country were shut and thousands of extra police officers were on duty to quell anticipated violence during the national strike.
Jamaat-e-Islami and its student wing Islami Chhatra Shibir activists resorted to hit-and-run tactics, a report by the newspaper The Daily Star said. Incidents of clashes, arson on shops and vehicles and vandalism across the country have been reported.
More than 70 demonstrators were arrested around the country and police in Dhaka detained 69 Jamaat-Shibir activists.
Also in Dhaka, a U.S. Embassy vehicle parked on the street was torched, the Star report said. No injuries were reported.
Last week the main opposition party Bangladesh Nationalist Party warned the governing Awami League party that a non-stop strike will ensue if it didn't meet the opposition's demands to set up a caretaker government ahead of general elections by January 2014.
The Awami League has been swamped with allegations of corruption and embezzlement of public funds.
The BNP leads an opposition alliance of 18 parties including Jamaat-e-Islami. BNP chairwoman Khaleda Zia, who served three terms as prime minister of Bangladesh, said her party would observe protest programs, including a countrywide road blockade Dec. 9 to press its demands, The Daily News said.
Zia said she would lead a major protest procession Dec. 26 in the capital, while other leaders of the 18-party alliance march with protesters in their representative areas.
Zia claimed she had information and the names of ruling party leaders who had embezzled public money and where they kept it, The Daily Star reported.
Political tensions increased in May after Motiur Rahman Nizami, head of Jamaat-e-Islami, and former party leader Ghulam Azam were charged with war crimes and atrocities during the country's 1971 independence struggle against Pakistan.
The Awami League-led government set up the special International Crimes Tribunal to try Bangladeshis accused of collaborating with Pakistani forces that attempted to stop Bangladesh from becoming an independent country.
Several hundred thousand people died in the war, researchers said.