North Korea said this month it would fire a rocket to put a satellite into orbit between April 12 and 16 to mark the 100th anniversary of the birth of founding president Kim Il-Sung.
But the United States and its allies suspect the launch is a disguised missile test, and said it would contravene UN sanctions aimed at curbing North Korea's missile program.
"I issued a destroy order," Defense Minister Naoki Tanaka told reporters in Tokyo, saying he had received the green light to shoot it down.
The order was issued after Prime Minister Yoshihiko Noda's cabinet approved it on Friday morning.
Last week Tanaka said he was readying Japan's missile defense systems but Friday's approval gives the military the power to destroy the rocket if necessary.
He said last week surface-to-air interceptors would be deployed on the southern island chain of Okinawa, over which Tokyo believes the projectile may pass, and in central Tokyo, one of the world's biggest cities.
In 2009, Japan ordered missile-defense preparations before Pyongyang's last long-range rocket launch, which brought UN Security Council condemnation and tightened sanctions against the isolated communist state.
That rocket, which North Korea said was also aimed at putting a satellite into orbit, passed over Japanese territory without incident or any attempt to shoot it down. - Agence France-Presse