The protesters had erected a barricade on a major highway connecting the capital, Dhaka and the southern port city of Chittagong, and violence erupted when police tried to break up the crowd, according to a statement by the Dhaka Metropolitan Police.
Ten police officials were among the injured, the statement said.
The protesters said they took to the streets as they were not getting adequate water and electricity over the past few weeks in Dhaka's Demra area, local journalist Shamim Ashraf told The Associated Press by phone from the scene.
He said a lawmaker from the ruling coalition of Prime Minister Khaleda Zia was also injured during the melee.
At least 15 injured people were hospitalized, the United News of Bangladesh agency reported.
Supplies of water are not adequate in Dhaka, a city of 10 million people, and most areas in the capital remain without power for hours everyday.
Bangladesh produces about 3,000 megawatts of electricity against total demand of around 4500 megawatts, according to the government's Power Development Board.
At least 18 people have been killed by police since January in southwestern district of Chapainawabganj during protests over power shortages.
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