Households across the island were affected, including 490,000 in the capital Taipei.
By Thursday afternoon, 70 per cent of the affected homes had regained power.
President Tsai Ing-wen apologizaed for the inconvenience caused by the accident and demanded a speedy investigation.
It was caused by an outage at Hsinta Power Plant, which sits in Kaohsiung City in the south of the island, according to Taiwan's cabinet, the government's executive branch.
Cabinet spokesman Lo Ping-cheng told a news conference on Thursday that the reserve power remained at about 24 per cent but that failures at the plant caused problems in the transmission and distribution of power to the central and northern parts of the island.
Lo said the incident shows the vulnerability of power transmission from the south to the north and the urgent need for Taiwan to finish construction of a liquefied natural gas terminal in the north.
Power supply to the science parks, which are home to Taiwan's essential tech industries, was unaffected, the state-run Central News Agency (CNA) reported.
A nuclear power plant in southern Taiwan went offline for safety reasons, CNA said.
The state-run Taiwan Power Company said in the evening that rolling power cuts persisted in parts of southern Taiwan as some problems remained unsolved and the electricity generated by solar power was reduced after sunset.
About 1.07 million households in southern Taiwan were still left without electricity by late on Thursday, CNA reported.
Local media showed images of dark streets and traffic jams in several cities as traffic lights remained off.
More than 250 incidents of people stuck in elevators were reported to the police.
Train and metro services, which had been initially slightly affected by the incident, gradually resumed normal service.
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