Leader Kim Jong Un oversaw the test himself, KCNA reported on Saturday (Friday evening, ET).
A submarine launched the missile at a location far from the North Korean mainland, according to the news agency.
Kim praised the test as a "miraculous achievement" and said his country is capable of producing this type of missile. This missile was a "time bomb which will go off on the backs of our hostile enemies at any time," he added, the KCNA report said.
Such rhetoric, while alarming on its face, is not unlike Kim's pronouncements after missile tests in the past.
While declining to talk about any specific "intelligence matters," a U.S. State Department official said more generally that "launches using ballistic missile technology are a clear violation of multiple UN Security Council resolutions."
"We call on North Korea to refrain from actions that further raise tensions in the region and focus instead on taking concrete steps toward fulfilling its international commitments and obligations," the official said.
Analyst: Hard to defend submarine missiles with nuclear warheads
North Korea has already allocated a significant portion of its budget to the military, and Saturday's announcement does not necessarily signify a ramping up of military efforts.
Daniel Pinkston, deputy project director for North East Asia at the International Crisis Group think tank, told CNN that, if authentic, the latest missile test "would be quite significant," since North Korea has been working on these capabilities for decades.
"If they can deploy an operational submarine that could launch ballistic missiles armed with nuclear warheads, it would give them a pretty credible second strike capability, and it's difficult to defend against. So it would give them the kind of deterrent that they have said they wish to have," he said.
"Everyone knew they had been working on this. I think actual flight test is sooner than people had expected."
Also Saturday, a South Korean defense ministry official said North Korea had fired three ship-to-ship missiles from the sea near North Korea's eastern city of Wonsan.
No other details were available as of yet, the official said. The missiles were fired in an hour-long window Saturday afternoon local time (between 3:25 and 4:23 a.m. ET.)
The anti-ship missiles are designated KN-01 type by South Korea, and are not in the same category as the submarine-launched ballistic missile reportedly tested by the North. That launch was from a port farther to the north, up the eastern coast of the Korean Peninsula.
News of the latest missile firings come one day after North Korea threatened to attack,
without warning, any South Korean naval ships that entered disputed waters west of the peninsula.
South Korea responded by threatening to retaliate if North Korea carries out any acts of aggression.