The authorities in Kagoshima City, Kirishima and Aira have urged their residents to move to safety immediately.
One elderly woman in Kagoshima City died after a mudslide hit her home.
Prime Minister Shinzo Abe has told residents of the cities to “take steps to protect their lives”.
Kagoshima prefecture has asked Japan’s Self-Defence Forces to help with the relief efforts.
About 310,000 residents in the neighbouring Miyazaki prefecture have also been advised to evacuate.
Weather officials say 39 inches of rain have fallen on Kyushu Island since last Friday, and Japan’s Meteorological Agency forecasts the rains will continue into next week.
More rain is expected in the southern part of the island by midday tomorrow, with some areas predicted to get heavy rains every hour.
Last July about 200 people died in western Japan in the country’s worst flooding disaster in decades. It was the highest death toll caused by rainfall in Japan since 1982.
About two million people were evacuated and more than 70,000 emergency workers were deployed after the heavy rain caused floods and landslides in the region.