Staff at the official residence - known as "the Kantei" - discovered the 50-centimetre (20-inch) craft on top of the five-storey structure in central Tokyo yesterday morning.
A plastic bottle with the internationally-recognised symbol for radioactivity was attached and traces of radiation were detected.
No one had been on the roof since Prime Minister Shinzo Abe used the helipad on March 22, reports said, citing unnamed investigative sources.
The drone was dry when it was found, indicating that it landed on the roof after April 20 when it last rained in Tokyo, Kyodo News and the Yomiuri Shimbun reported.
The drone was made by major Chinese manufacturer DJI, other local reports said.
There are currently no legal restrictions on the use of drones - which is becoming more common in Japan, particularly for aerial surveying, photography and video shoots.
Chief Cabinet Secretary Yoshihide Suga said today the government will consider regulating drone flights "as soon as possible."
The government has instructed police to beef up monitoring of airspace above important facilities, including nuclear power plants and airports, reports said.
