There are reports of many smaller demonstrations elsewhere in the capital and in other towns and cities.
"We have spent two nights without electricity... Children are falling sick, everybody's life is becoming a hell," Azad Majumder, a resident of Mirpur, told Reuters news agency.
Discontent over electricity has been growing in Bangladesh where the poor power supply has recently got much worse.
People have been particularly angered by black-outs during special evening prayers during the holy month of Ramadan.
The BBC's Roland Buerk in Dhaka says years of neglect and corruption have been blamed for many power stations going out of order.
In response to the riots, the government has deployed extra security personnel to protect distribution offices.
Lighting on advertising billboards has been banned and some factory owners have been told they will not get any power after dusk.
