Analysts say North Korea has several nuclear warheads but this development would be an advance as submarine-fired devices are difficult to detect.
This latest test has not been independently verified.
The US said using ballistic missiles was a “clear violation” of UN sanctions against North Korea.
A statement from the State Department made no comment on the reported test but called on North Korea “to refrain from actions that further raise tensions in the region”.
State media described the missile emerging with “a fiery, blazing trail”, but did not mention the date or the location of the test.
The North Korean leader, Kim Jong-un, was pictured apparently overseeing the launch.
Mr Kim said his country now possessed a “world-level strategic weapon capable of striking and wiping out in any waters the hostile forces infringing upon [North Korea’s] sovereignty and dignity”, the reports said.
After the announcement, South Korea said the North fired three anti-ship cruise missiles into the sea off its east coast.
Pyongyang had warned it would fire without warning against vessels it claims have violated its waters.
South Korea is yet to comment on the missile test, but the country’s National Security Council has met in emergency session.
Claims about North Korea’s military capabilities always have to be treated sceptically. The latest pictures in the state-run media may or may not be photo-shopped, perhaps to insert Kim Jong-un very prominently into the picture of a missile launch.
However, analysts at the respected US-Korea Institute at Johns Hopkins University in the US reported recently that satellite pictures indicated that “the conning tower of a new North Korean submarine first seen in July 2014 houses one to two possible vertical launch tubes for either ballistic or cruise missiles”.
The academics also said that satellite imagery indicated “that North Korea has been upgrading facilities at the Sinpo South Shipyard in preparation for a significant naval construction program, possibly related to submarine development”.
Missiles launched from submarines dramatically change the calculation that any potential target must make because the warning time is so much shorter than with land-based missiles with which preparations on the ground might also be detected.
The best estimate of North Korea’s nuclear arsenal is that it could make up to 20 weapons but that its ability to make them small enough for a missile is unclear.
It is clear, however, that the ambition is there – not least because the North Korean foreign ministry said so: Its nuclear forces were a “powerful, treasured sword” to “protect the sovereignty of the country”.