Authorities in Hiroshima and the northern part of Kyushu issued their highest evacuation alert as the weather agency reported unprecedented levels of rain in the area.
Under the non-compulsory alert, around 1.4 million residents have been asked to leave their homes immediately, public broadcaster NHK reported.
TV footage showed rescuers towing residents through submerged streets on a lifeboat in the town of Kurume in Fukuoka, while a muddy stream began to overflow in neighbouring Saga prefecture.
A 59-year-old woman died and two of her family members were missing after a landslide destroyed two houses in Unzen, Nagasaki prefecture, a local official said.
“More than 150 troops, police and firefighters were dispatched to the site for rescue operations,” Takumi Kumasaki told AFP.
“They are carefully searching for the missing residents, while watching out for further mudslides as the heavy rain continues.”
Downpours are forecast for several more days over a large swathe of the country.
Scientists say climate change is intensifying the risk of heavy rain in Japan and elsewhere, because a warmer atmosphere holds more water.
“Unprecedented levels of heavy rain have been observed,” Yushi Adachi, a meteorological agency official, told reporters in Tokyo.
“It’s highly likely that some kind of disaster has already occurred,” Adachi said.
“The maximum alert is needed even in areas where risks of landslides and flooding are usually not so high.”
Downpours last month caused a devastating landslide in the central resort town of Atami that killed 23 people, with four still missing.
And in 2018, more than 200 people died as floods inundated western Japan during the country’s annual rainy season.