Defense Minister Itsunori Onodera issued the order, which took effect on Thursday and runs through April 25, the day that marks the founding of North Korea's army, the source told Reuters on condition of anonymity.
Following the order, meant "to prepare for any additional missile launches," a destroyer was dispatched to the Sea of Japan and will fire if North Korea launches a missile that Tokyo deems in danger of striking or falling on Japanese territory, the source said.
Tensions have been building between North Korea and its neighbours since Pyongyang – in an apparent show of defiance – fired two Rodong missiles on March 26, just as the leaders of Japan, South Korea and theUnited States were sitting down to discuss containing the North Korean nuclear threat.
That first firing in four years of mid-range missiles that can hit Japan followed a series of short-range rocket launches over the past two months. The Rodong ballistic missiles fell into the sea after flying 650 km (400 miles), short of a maximum range thought to be some 1,300 km, Japan said.
Since then, North Korea has rattled sabres by firing artillery rounds into South Korean waters, prompting the South to fire back; South Korea has test-fired a new ballistic missile with a range of 500 km; and Pyongyang has threatened an unspecified "new form" of nuclear test.
At the same time, Japan and North Korea resumed talks - suspended since Pyongyang test-launched a long-range missile more than a year ago - over the North's nuclear and missile programmes, as well as the fate of Japanese abducted in the 1970s and 1980s to help train North Korean spies.
Onodera has avoided publicly announcing the new missile-intercept order so as not to put a chill on those talks, Japanese media said.
He also did not deploy Patriot missile batteries that would be the last line of defence against incoming warheads, the source told Reuters.
Japanese Aegis destroyers in the Sea of Japan are equipped with advanced radar equipment able to track multiple targets and carry missiles designed to take out targets at the edge of space.
Writing by Tim Kelly and William Mallard