Police had to fire rubber bullets and teargas canisters to disperse the unruly activists.
The protesters exploded 15 cocktail bombs in Rajshahi, Barisal, Bogra and Chittagong and blocked different roads to observe the shutdown.
They also torched and vandalised at least 34 vehicles in Comilla, Rajshahi, Pirojpur and Chittagong.
Police detained at least 34 people from different parts of the country on charges of plotting subversive activities, attacking law enforcers and damaging vehicles.
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"We are making a clarion call to observe the nationwide general strike to protest the blueprint to kill the jailed top Jamaat leaders," the party said in a statement.
Earlier, a huge posse of security personnel, including Rapid Action Battalion, were deployed at key points in Dhaka to prevent violence.
On August 1, the Bangladesh High Court had banned Jamaat from contesting future polls, leaving the once-most powerful fundamentalist party with an uncertain future. The court also cancelled its registration with the Election Commission.
The verdict came at a time when the demand for outlawing the party, blamed for war crimes during the 1971 liberation war against Pakistan, was mounting.
Several top Jamaat leaders, including its 91-year-old supremo Ghulam Azam, were recently sentenced either to death or to long jail terms for masterminding atrocities during the war.