Defence Minister Gen Nakatani issued the order, the Nikkei daily and Kyodo News reported, after reports of suspicious activity at Pyongyangs main satellite complex fuelled speculation a launch could come as early as next week.
A Japanese defence ministry spokeswoman declined to confirm the report when contacted by AFP, saying that "would reveal our strategy".
"But we are taking all possible measures to respond (to a missile launch) by collecting information and coordinating with countries concerned," she added.
North Korea is banned from using ballistic missile technology by UN Security Council resolutions, so any launch would further raise tensions among the international community only weeks after its latest nuclear test.
Two US defence officials confirmed to AFP on Friday there was ongoing activity at the Norths Sohae satellite complex, which Pyongyang has been upgrading to handle larger, longer-range rockets since 2013.
Their comments came after Japans Kyodo News, citing an anonymous government source, said satellite imagery showed increased movement at Sohae that could suggest a launch as early as next week.
Also on Friday, Japanese Foreign Minister Fumio Kishida held telephone talks with US Secretary of State John Kerry about the possible launch.
"We cant deny the possibility that North Korea will take further provocative action," Kishida told reporters, adding that he and Kerry had "exchanged information on how to cooperate from now on".
Japan deployed surface-to-air missile defences in 2012, the same year North Korea put a satellite into orbit with its Unha-3 carrier.
Although Pyongyang insisted it was a purely scientific operation, that launch was condemned by the international community as a disguised ballistic missile test and resulted in a tightening of UN sanctions.