Twelve of the casualties were reported in and around Wenzhou city in the province of Zhejiang, where downpours caused mudslides and several houses collapsed on Saturday night, Xinhua news agency said.
It added that in the neighbouring city of Lishui, two people were also killed.
Xinhua quoted local disaster relief officials as saying the dead and missing may have been washed away by floods or buried under ruined homes.
About 1.58 million people in the city were affected by the typhoon by Sunday afternoon, the agency said, estimating direct economic losses at $644 million.
Nearby Wencheng county saw downpours of 645 millimetres (25.4 inches) in 24 hours -- the heaviest in 100 years — after the typhoon made landfall on Saturday night, according to earlier Xinhua reports.
The storm had landed in Fujian province and initially cut power to more than three million homes there, according to the agency, but more than a third had electricity restored by Sunday morning.
Billed as the biggest typhoon of the year last week with winds of up to 230 kilometres an hour, Soudelor — named after a legendary Micronesian chief — has since weakened.
China's National Meteorological Center forecast the typhoon would be downgraded to a tropical depression by Sunday night as it moved further inland.
Soudelor left six people dead in Taiwan, where it ripped up trees and triggered landslides, damaging electricity lines and knocking out power to a record four million households.
Almost half a million homes were still without power on Sunday, Taiwan Power Co. said, as blocked roads hampered efforts to restore supplies in some areas.
Taiwan's death toll rose to six after an eight-year-old girl who went missing Thursday after being swept out to sea with her mother and twin sister was found dead.
Her mother and sister, caught in the strong waves on the east coast, were the first victims of the typhoon. Some 379 people were injured by the storm in Taiwan, which saw rivers break their banks under torrential rain and towering waves pound the coastline.
Taiwan lifted its typhoon warning Sunday, but the weather bureau warned of further heavy rain in the south.
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