Police said they opened fire when strikers attacked an officer with sharp objects in Meherpur district.
The firing left one dead, local media reported.
Other districts also witnessed vandalism, explosions and detention as the strike stepped into second consecutive day.
A senior leader of Meherpur Jamaat unit said another party cadre, who was injured during the clash, succumbed on way to hospital.
Yesterday, one person was killed and several others injured in the violent protests.
Jamaat enforced the 48-hour strike from yesterday to protest the Supreme Court verdict on its leader 65-year-old Abdul Quader Mollah.
The apex court on Tuesday sentenced Jamaat assistant secretary general Mollah to death, overruling the judgment of a special tribunal that had given him life term for war crimes committed during the country's 1971 liberation war.
This is the first such case which came for the apex court review while two war crimes tribunals are trying the high profile accused of "crimes against humanity" during the war, mostly belonging to Jamaat, which was opposed to the country's independence from Pakistan.
The two tribunals have already handed down death penalty to four and long term or life imprisonments to two others.
Officially three million people were killed in the liberation war during which Jamaat allegedly masterminded the murders of the country's leading intelligentsia including professors, doctors and journalists.