In Hyogo, 500km west of Tokyo, the heavy downfall triggered floods and landslides.
Police said about 2,200 people were evacuated from their homes and were staying at public schools.
About 500 houses were flooded and residents worked to clear mud and water from their homes with shovels and buckets.
Japan's meteorological agency warned of further heavy rain and landslides in eastern Japan as Etau moves across the country.
The agency forecast the typhoon would skim just east of heavily populated Tokyo on Tuesday afternoon.
Rain, floods, mudslides, heavy seas and winds gusting to 126kph were expected in many regions.
Some residents in the capital put precautionary sandbags around their homes on Monday evening.