The agency predicted as much as 50 centimetres (20 inches) of rainfall by midday Monday, warning of flooding and landslides.
The agency also warned residents in the affected area of “unprecedented” levels of powerful winds and waves, urging them to evacuate early.
Local authorities so far reported no major damage or injuries.
In the hard-hit Kagoshima prefecture, more than 9,000 residents took shelter at evacuation centres on Sunday. In the neighbouring Miyazaki prefecture, another 4,700 people were evacuated.
Kyushu Electric Power Co. said more than 93,000 homes across the Kyushu island were without electricity on Sunday because of damage to power lines and facilities.
Footage on NHK television showed a pachinko pinball parlour with part of its glass wall shattered by the gust in Kanoya city in Kagoshima.
Elsewhere in the prefecture, an elderly woman suffered a minor injury as she fell, NHK said.
Hundreds of domestic flights in and out of the region have been cancelled and more are planned to be grounded in western Japan through Tuesday as the typhoon headed northeast, according to Japan Airlines and All Nippon Airways.
Public transportation including trains and buses in Kagoshima and Miyazaki were suspended throughout Sunday. Railway operators said bullet trains on the Kyushu island have been suspended.
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