Moon immediately convened an emergency meeting of his national security council to discuss the launch.
It also comes after repeated warnings from US President Donald Trump to North Korea to stop - and China to crack down on its errant neighbour. Trump will likely urge Beijing to use its leverage over Pyongyang to punish it for this latest provocation.
In a statement, the White House said: "North Korea has been a flagrant menace for far too long ... Let this latest provocation serve as a call for all nations to implement far stronger sanctions against North Korea. With the missile impacting so close to Russian soil - in fact, closer to Russia than to Japan - the President cannot imagine that Russia is pleased."
Analysts were working to identify the kind of missile launched. Japan's Defence Minister Tomomi Inada told reporters there is a possibility that it was a new type of ballistic missile, saying it flew for about 30 minutes and at an altitude exceeding 2000km. She says more analysis was needed.
US Pacific Command, based in Hawaii, said it had detected and assessed the missile, and "the flight was not consistent with an intercontinental ballistic missile". However, it did not state what kind of missile it appeared to be.
South Korea's Joint Chiefs of Staff said that the missile was fired from Kusong, an area not far from the border with China.
North Korea has been testing missiles at a rapid rate over the past year. The two most recent launches last month were deemed to have failed, as they exploded within seconds.
North Korea launched two missiles in October last year from an air base in Kusong on North Korea's west coast, on the other side of the country from the usual intermediate-range Musudan test site near Wonsan, on the east coast. US Strategic Command said they were "presumed" to be Musudans, which are technically capable of flying as far as 3860km. But Jeffrey Lewis, director of the East Asia nonproliferation programme at Monterey in California, said at the time that there was an "even chance" that they were ICBMs.
At a huge military parade that Kim presided over last month, North Korea displayed two of its newest model missiles. Although there are still plenty of technical hurdles to be overcome, many analysts believe North Korea will eventually achieve Kim's stated goal of developing an ICBM that can reach the mainland US.
- Washington Post, AP