Power was restored in some parts of the capital several hours after the outage began and authorities said they hoped to have electricity back on across the densely populated nation by Saturday evening.
Engineers "are working to fix the outage" which hit all areas linked to the national electricity grid, Masud Alberuni, a senior power ministry official, told AFP.
"The national grid tripped" close to mid-day, Alberuni said.
"As a result, all the power generating stations automatically shut down," he said.
The outage marked "the first time the country has been without power since 2007" when Bangladesh was hit by a devastating cyclone, Alberuni said.
Saturday is a weekend day in Bangladesh so the impact on industry was not as severe as if the blackout had occurred on a weekday.
Also the weather is getting cooler so the lack of air conditioning and fans was not such a problem.
But homes and shops were without electricity to power appliances and elevators were halted.
Hospital intensive care units were functioning on back-up generators.
Dhaka international airport was also running on generator fuel, the power ministry official said.
"We have already restored power to some parts of the capital and we can hope we can restore power to the whole country by the evening," power development board spokesman Saiful Hasan told AFP.
Power ministry official Alberuni did not identify the transmission line which had suffered the problem.
But Bangladeshi media reported that it involved a transmission line transporting electricity from India to its northeastern neighbour.
Dhaka began importing power from India late last year through a transmission line stretching from India's eastern state of West Bengal to southwestern Bangladesh.
Electricity supplies in Bangladesh, one of the world's poorest countries, are vastly stretched.
Growth in energy consumption has outdistanced economic growth in Bangladesh, as in other parts of the developing world, with an expanding middle-class and increasing industrialisation imposing ever-heavier loads on scant fuel-generating capacity.
The outage evoked memories of a power blackout in India two years ago that was one of the world's worst in recent times.
The Indian outage sparked serious doubts about the ability of the country's rickety electricity infrastructure to meet its aspirations to transform itself into an economic superpower.
Two-thirds of India's states suffered power cuts, along with the capital New Delhi, when three of the country's five power grids failed at the same time.
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