State power company Taipower said a transmission pylon on a hill in New Taipei city toppled during torrential downpours, causing a reactor at a nuclear plant there to cut out.
A second reactor automatically shut down as safety measures were activated and neither were damaged, it added.
Water surged into cars, homes and businesses after 600 millimetres of rain fell in under 11 hours in some areas.
Rescuers found the body of a female motorcyclist who had been washed into a ditch in New Taipei City, one of the worst hit areas.
The National Fire Agency said at least five people were hurt in the deluge, including a driver injured when his truck overturned and another man hurt after being buried in a mudslide.Two people, one from New Taipei City and the other from the city of Keelung are missing after being swept off, the agency said, while a road bridge in the area was smashed in half by a swollen river.
Some 15 hikers were also stranded on a mountain in central Miaoli because of a surging river, but were thought to be unharmed and with sufficient supplies.
Rescuers used rafts to help evacuate residents in Keelung and one young girl waiting at a bus stop there was rescued and hospitalised after being washed away.
Cars sank window-deep in the floods across the north while people tried hopelessly to bail out their water-logged shops and houses.
Traffic came to a standstill as vehicles were abandoned, with television footage showing passers-by desperately holding on to a floundering motorcyclist.
At a kindergarten in Taipei, 53 children had to be evacuated as flood water poured in, local media said.
One man in the capital told reporters how he had tried to shelter in a park pavilion, but became surrounded by water.
"I was just staying (in the pavilion) for the rain to stop -- I didn't think it would get so heavy," he said.
The rain started late Thursday and was easing up in Taipei by Friday afternoon, but the island's Central Weather Bureau warned it would now move south towards the centre island.
Further heavy rain Friday and Saturday would particularly affect the west of Taiwan, which should take "serious precautions", the bureau said.
At least 258 local and international flights had been cancelled or postponed due to heavy rain, aviation authorities said.
At the city's main international airport in Taoyuan, a shopping area inside the terminal building flooded as rain poured through the roof.
Thunderstorms forced the capital's smaller Songshan airport to shut down for two hours.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)