Highest-level rain warnings have been issued in a number of prefectures, including Fukuoka and Hiroshima.
One woman is dead and her husband and daughter are missing after a landslide destroyed two homes in Nagasaki prefecture amid the bad weather.
More than 150 troops, police, and firefighters have been sent to help with rescue operations in the area.
“They are carefully searching for the missing residents while watching out for further mudslides as the heavy rain continues,” a local official told the AFP news agency.
The west of the country is worst affected but heavy downpours are expected across the country in the coming days.
Yushi Adachi, from Japan’s meteorological agency, described the current rainfall as “unprecedented”.