coastal townships, the government said.
Evenings papers said it was the county's worst flooding in 50 years, citing Pingtung's magistrate Tsao Chi-hung, while his deputy Chung Chia-pin told TVBS that an estimated 8,000 people were trapped in flooded areas.
Hundreds of rescuers and solders continued to battle the bad weather in Pingtung to evacuate people to safety and deliver supplies, the authorities said.
Television footage showed torrential downpours had submerged houses and streets in Pingtung, cutting off electricity and phone services.
"The flood started this morning and the water is over two stories high in most places," said a policeman from Chiatung township, one of the worst-hit areas in Pingtung with some 10,000 residents.
In southern Kaohsiung city, a woman died after she fell into a ditch when strong winds swept her off her motorcycle, said the National Fire Agency, which coordinates rescue work.
It also said four fishermen and a 50-year-old woman who had fallen into a river were unaccounted for while seventeen people have been injured but none seriously.
Taiwan's worst flooding occurred exactly 50 years ago when 667 people were killed as heavy rains lashed the island for three consecutive days beginning on August 7.
Morakot made landfall around midnight Friday in eastern Hualien county, unleashing powerful winds that swayed high-rise buildings, turned over cars and uprooted trees and road signs in many places.
Waves as high as nine metres (30 feet) hit coastal Hualien, reports said, while television footage showed winds had ripped the iron roof off an elementary school in central Changhua county.
The typhoon had caused at least 832 million Taiwan dollars (26 million US) in agricultural damage and temporarily disrupted electricity in more than one million households, officials said.
Taiwan's financial markets, offices and summer schools were shut and most outdoor festivities postponed on Friday while nearly 600 domestic and international flights were cancelled in two days, the authorities said.
According to Taiwan's weather bureau, Morakot was 80 kilometres (50 miles) north-northwest of Taipei at 17:30 pm (0930 GMT), moving north-northwest at 11 kilometres per hour and packing gusts of 108 kilometres per hour.
The bureau has downgraded Morakot to a tropical storm but warned against continuing heavy rains in southern Taiwan as it churned towards southeast China.
Across from Taiwan, in Fujian, 21,190 people were evacuated to safety and about 34,000 vessels had been recalled to port ahead of the typhoon, according to provincial authorities.
Fujian's meteorological station said Morakot was likely to land on the coastal province Saturday evening or night.
In Fujian's Putian City all scenic sites and ports were closed and school classes suspended. A team of 26,222 people had been formed and equipped with flood-control materials, said Huang Dongzhou, director of the city's flood control office.
In adjacent Zhejiang Province, nearly 300,000 residents and tourists in danger areas were evacuated, ships were recalled to harbor and the local government said soldiers were prepared for emergencies.