The government set up a special unit within Prime Minister Shinzo Abe's office to coordinate Japan's response to the latest development, Chief Cabinet Secretary Yoshihide Suga told reporters.
"We are doing all we can, including dispatching a Coast Guard unit" to remove the oil, he added.
Amami-Oshima is part of a chain of islands that includes Okinawa, an area famous for pristine beaches and reef systems.
The Iranian tanker sank nearly three weeks ago, raising worries about damage to the marine ecosystem.
The bodies of two sailors were recovered from the ship while a third body was pulled from the sea near the vessel. The remaining 29 crew of the ship are presumed dead.
Earlier, the Chinese government said the sunken tanker had created two oil slicks. The ship, which was almost 1 million barrels of condensate — an ultra-light, highly flammable crude oil — sank after several explosions weakened the hull.
Japan's environment ministry had said last month it saw little chance that the spill would reach the country's shores.