Local media reports the downpour has caused flooding that has also damaged homes and bridges.
This has prompted calls for the authorities to open evacuation shelters after residents were ordered to leave the area.
A state emergency management official says the rains have led to the cresting of the Kaupakalua Dam on the island's northern region of Haiku.
Governor David Ige says evacuation shelters have opened at a community centre and a high school.
