It was the first reported incident of its kind.
Japan's Air Self-Defence Force sent an unspecified number of jets to the area, the official said.
The drones did not enter Japanese airspace, the official said.
A second Japanese defence ministry official said the nationality of the drone was not clear, but added that it came from the northwest and and was last seen flying back in that direction.
China does have drones but when asked about the incident, foreign ministry spokesman Hong Lei said: "I am not aware of the situation."
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And two weeks ago, fighters were dispatched to head off a Chinese government plane flying towards the Senkaku islands, which Beijing calls the Diaoyus and claims as its own.
A Y-12 propeller plane flew about 100 kilometres (60 miles) from airspace around the islands on August 26, before heading back towards China after Japan's military planes became airborne.
In December, a similar plane from China's State Oceanic Administration breached airspace over the disputed islands, prompting the launch of Japanese F-15s.
Friday's reports came as four Chinese coastguard ships sailed in the so-called contiguous zone that surrounds territorial waters around the islands.
It was the latest in a series of such sorties by Chinese government ships since Tokyo nationalised three islands in the chain last September, reigniting a long-simmering dispute.