The activists of the former prime minister Khaleda Zia's party allegedly hurled stones on the two victims.
Witnesses and police said the activists threw stones on a covered van which was carrying the schoolteacher, Shamsun Nahar, and her husband to the northeastern Noakhali town.
"She was hit on the head by a stone and doctors at a nearby hospital declared her dead as she was rushed to the facility," a police official said.
Nahar's husband Shahjahan Siraj was also injured in the attack. He was travelling to Noakhali to join his workplace while "they (activists) started hurling stones as we reached Maijdi Municipal Bazar area."
BNP and its right wing allies in 20-party coalition, including fundamentalist Jamaat-e-Islami, called for the daylong stoppage after government banned all political rallies in Gazipur on the outskirts of the Bangladeshi capital, after
BNP and ruling Awami League's student wing planned rival demonstrations at the same venue.
BNP Spokesman Ruhul Kabiar Rizvi claimed at least 30 of their leaders and activists were detained by the police during the strike hours across the country and forced many others to go into hiding to evade harassment.
Several Party supporters clashed with police in Dhaka and vandalised at least seven vehicles injuring three policemen and a local in the incident.
"Three of our colleagues were injured as they attacked us with cocktail bombs. They are being treated at the Razarbagh police hospital," a police spokesman said.
The public and private vehicular movement was disturbed due to strike.

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