Tens of thousands of workers rioted during protests over low wages protested in Dhaka and the south-eastern city of Chittagong, police said.
On Saturday the country's largest exporter, Korean company Youngone, shut down all 17 of its factories following demonstrations by its employees.
Bangladesh's garment workers make clothes for many Western brands.
They say that a government-ordered wage rise that was due last month has not been implemented.
"Three people have died, including a rickshaw driver died on the spot after he was hit by a brick," Meshbahuddin, the special branch police chief of Chittagong who only uses one name, told the AFP news agency.