Rainwater also leaked into some competition venues, with more wet weather forecast for the coming days.
About 104 mm (four inches) of rain fell in an hour in part of Nagoya on Tuesday, prompting municipal officials to issue an evacuation order for parts of the city.
Cars were forced to plow through heavily flooded roads, causing huge jams, while water streamed into subway stations.
Scientists say human-induced climate change is increasing the frequency and intensity of weather events in Japan and elsewhere.
There is no dedicated athletes' village at this year's Asian Games, with organizers instead relying on a cruise ship, temporary wooden containers and hotels.
