One person in Butuan City was killed after being hit by a tree uprooted by the storm's 80-kilometre per hour winds, village chief Fred Olaer said.
In Surigao del Sur province on Mindanao island where the storm known locally as 'Seniang' hit land before dawn, 13,740 people were evacuated in eight towns, Governor Johnny Pimentel told AFP.
"The rains are very strong and there has been no let-up in the last three days," Pimentel said.
Flood waters as deep as five feet (1.5 metres) were reported in some areas as rescuers in rubber boats rushed to aid residents trapped in their homes, he said.
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The number of evacuees may rise as rivers continue to swell, he said.
Winds had brought down trees and blown roofs off shanties, he said.
"This is the first time that my house was flooded," Agusan del Sur Vice Governor Santiago Cane said by phone.
Thousands of others were evacuated from lakeside and riverside communities in Agusan del Norte, said provincial disaster office staffer Erma Suyo.
The storm, moving west at 11 kilometres per hour, is expected to cross the central Philippines in the next two days.
The storm forced the cancellation of 32 domestic flights, the Manila airport authority said.
Hundreds were stranded in seaports in the south, police said.
The affected provinces are located in the Caraga region in northeast Mindanao, one of the Philippines' most flood-prone areas.
The Philippines is battered by about 20 storms every year, many of them deadly.