Economic Affairs minister Lee Chih-kung tendered his resignation verbally to Premier Lin Chuan, United Daily News reported, citing a Cabinet spokesman. Lin accepted the resignation, the spokesman said according to the daily.
As many as 6.68 million households and commercial units saw their power supply cut or disrupted on Tuesday after "human error" disrupted natural gas supply at a power plant in northern Taiwan's Taoyuan, the semi-official Central News Agency reported, citing the government-controlled oil company CPC Corporation as saying.
The company added that power at the plant, Taiwan's biggest natural gas power plant, resumed two minutes later.
In New Taipei City, there were at least 27,000 reported cases of people being stuck in lifts.
Photos in social media also showed huge crowds stranded in lift lobby in Taipei's iconic 101-storey Taipei 101 building.
Power rationing was implemented beginning 6pm, Central News Agency said. Power supply was gradually being restored beginning at about 9:40pm. news reports said.
President Tsai Ing-wen apologised for the blackout, saying that she has ordered all relevant departments to produce clear report in the shortest time possible.
"Electricity is not just a problem about people's livelihoods but also a national security issue. A comprehensive review must be carried out to find out how the electric power system can be so easily paralysed by human error," said Ms Tsai in a Facebook post.
Taiwan has been at risk of a power shortage after a recent typhoon knocked down a power transmission tower in Hualien county along the eastern coast of Taiwan. This reduced the electricity supply by 1.3million kilowatts, or about 4 per cent of the operating reserve.
That was followed by the breakdown of a power generator at Taiwan's largest power plant, which further reduced the operating reserve by 1.5 per cent.
The situation is worsened by the ongoing heatwave that has hit Taiwan, with temperatures soaring to 38 degrees Celsius over the past week.
As a result, the government had imposed the rationing of electricity, like switching off all air-conditioning in many of its Taipei offices, a move that drew some public backlash.