The workers also set up roadblocks with burned tires and abandoned vehicles, disrupting traffic in the industrial towns of Gazipur and Ashulia, outside of Dhaka.
A protest leader, Delwar Hossain, said the workers were demonstrating peacefully and were attacked by police "without provocation."
Since the protests began in October, the government has deployed paramilitary border guards to boost security in Gazipur, a hub of several hundred garment factories.
Police said about 50 garment factories shut down for the day Tuesday because of the protests.
Garment workers in Bangladesh are poorly paid and are forced to work under poor and unsafe conditions in an industry that earns up to $20 billion a year about 70 percent of the country's export earnings.