Protesters blocked roads nationwide, demanding an independent body to oversee next year's election, a system that was done away with by the government last year, the BBC reported.
The main opposition party -- Bangladesh National Party -- called for the protests in an effort to urge the government to restore the system.
Police fired rubber bullets and tear gas while protesters threw petrol bombs, the BBC said.
"We allowed peaceful protests. But once they started attacking cars and buses and throwing cocktail bombs, we used non-lethal weapons such as rubber bullets and tear gas to disperse them," said Deputy Police Commissioner Imtiaz Ahmed.
Two protesters were killed in the clashes, while scores of others were injured, the BBC said.
Prime Minister Sheikh Hasina said Bangladesh disbanded the election system following a court order and has no intention of reversing the order.