The party's acting chief Mujibur Rahman made the announcement Saturday at a 20-party rally in Natore.
It comes a day ahead of its leader Mir Quasem Ali's verdict scheduled for Sunday.
Rahman alleged the government was plotting to eliminate its top brass.
"Prof Ghulam Azam has been tortured to death in prison. They are conspiring to eliminate our chief Motiur Rahman Nizami by unfairly handing him maximum penalty,” he said.
“We are enforcing shutdowns to protest this and will continue to do so. The general strike will continue until Thursday if there's another such verdict," he added.
War criminal Azam, who led the Jamaat during the 1971 Liberation War, died on October 23 at Bangladesh's top public hospital while serving a 90-year sentence.
Jamaat chief Nizami, a minister during the BNP-Jamaat coalition government from 2001-06, was sentenced to death for war crimes on Wednesday.
He led the notorious Al-Badr militia that spearheaded execution of intellectuals when Bangladesh was about to win independence.
The party, accused of committing war crimes during the war, called for a three-day strike – Thursday, Sunday and Monday – protesting the conviction.
Tuesday is a public holiday.
BNP chief Khaleda Zia and other top leaders of the alliance were on the stage when acting Jamaat chief Rahman spoke.
A large number of Jamaat activists took part in the rally but no banner or posters demanding release of its convicted leaders were seen.
He urged everyone to get ready for an anti-government stir under Khaleda's leadership.
"False cases, incarceration and police firing cannot suppress the people's movement. This government must bow out," Rahman said.
