Authorities suspended some train services and issued evacuation orders, warning people of possible landslides and flooding in 10 prefectures including the capital with some 25 million people.
Japanese public broadcaster NHK said 35 people were injured in central Japan, including a 93-year-old woman who broke her leg in a fall and two men who sustained light injuries after their car windshield shattered.
Japan's Meteorological Agency said the typhoon, currently a Category 1 storm, the weakest on a scale of 5, was potentially dangerous and could gather momentum as it passes over the ocean and heads toward heavily populated areas.
On Thursday, a 76-year-old man in central Japan was killed by a falling tree as he cleared away other toppled trees, the Kyodo News agency said.
Most of the injuries were caused by shattering glass as violent gusts broke windows of a commuter train in Chiba prefecture and of a hotel in Nikko late on Thursday.
As a precaution, authorities evacuated more than 1,200 residents from an area of Tokyo near the swollen Tamagawa River as scores of fire-fighters sandbagged the banks of the river.
Hundreds of public schools in central and eastern Japan were expected to close on Friday, NHK said.
On Thursday Fitow, packing winds of up to 126 kilometres per hour, also grounded more than 200 domestic flights at Tokyo's Haneda airport.
Airlines were expected to cancel more flights early on Friday.
The intensity of Typhoon Fitow, named after a flower in Micronesia, was just a notch below that of Typhoon Tokage, Japan's deadliest storm in 25 years that killed dozens in October 2004.