An opposition alliance led by the Bangladesh Nationalist Party is enforcing the strike to protest alleged police intimidation during a rally on Monday. Police later arrested some senior leaders and more than 100 activists in Dhaka.
The party is demanding restoration of a caretaker government system to oversee upcoming elections.
Its ally Jamaat-e-Islami wants a halt to trials of several opposition politicians accused of crimes stemming from the country's 1971 independence war.