The launch, which came as the US prepared to celebrate its Independence Day on the Fourth of July, was the latest in a series of provocations that have ratcheted up tensions over the nuclear-armed North's weapons ambitions.
The "unidentified ballistic missile" was fired from a site near Panghyon in North Phyongan province, the South's Joint Chiefs of Staff said in a statement, and came down in the East Sea, the Korean name for the Sea of Japan.
It flew for "several hundred kilometres", they added.
The device may have come down in Japan's exclusive economic zone, a spokeswoman for Tokyo's defence ministry told AFP - waters extending 200 nautical miles from its coast.
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Japanese Chief Cabinet Secretary Yoshihide Suga said the missile flew "for about 40 minutes" -- an unusually long flight time.
"This launch of a ballistic missile can never be tolerated, and Japan strongly protested to North Korea and condemned it," he told a briefing.
Pyongyang says it needs nuclear weapons to defend itself against the threat of invasion and has carried out multiple launches since Moon - who backs engagement with the North but also stresses the need for sanctions - was elected in May.
Moon called a meeting of the South's National Security Council in response to the launch.
At their summit in Washington at the weekend, Trump declared that the US had run out of patience with North Korea over its weapons drive, which includes developing a missile capable of delivering a warhead to the US mainland.
"Together, we are facing the threat of the reckless and brutal regime in North Korea," Trump said. "The nuclear and ballistic missile programs of that regime require a determined response.
"The North Korean dictatorship has no regard for the safety and security of its people, for its neighbours and has no respect for human life."
He later discussed the issue in separate phone calls with Chinese leader Xi Jinping and Japanese Prime Minister Shinzo Abe.
Shea Cotton, a researcher at the James Martin Center for Nonproliferation Studies in the US, suggested Tuesday's launch was deliberately timed to coincide with the anniversary of the US declaration of independence.
“It's already 4th of July in North Korea," he said on Twitter. "I somewhat suspect they're shooting off some fireworks today specifically because of that."
Washington, South Korea's security guarantor, has more than 28,000 troops in the country to defend it from its Communist neighbour, which has been intensifying missile tests.
There was also deep anger in the United States after Otto Warmbier, an American student who was detained in North Korea on a tourist trip around 18 months ago, was returned home in a coma in June, dying days later.
Trump had been pinning his hopes on China - North Korea's main diplomatic ally - to bring pressure to bear on Pyongyang but declared last week that their efforts had failed.
