Kim visited a navy fleet stationed on the east coast to inspect the test aboard a warship, KCNA said, without specifying the date of his trip.
The launch was aimed at verifying the "combat function of the ship and the feature of its missile system," while improving the sailors' capability to carry out an "attack mission in actual war," KCNA said.
"The ship rapidly hit target without even an error," it said.
Kim touted the ship for maintaining "high mobility and mighty striking power and constant preparedness for combat to cope with sudden situations," KCNA said.
The latest missile test came as South Korea and the United States are scheduled to stage the Ulchi Freedom Guardian summer exercises on Monday, designed to enhance their joint responses to North Korea's evolving nuclear and missile threats.
Pyongyang has denounced the allies' military drills as a rehearsal for nuclear war.
South Korea's military has said this year's exercises will be held on the "largest scale ever", mobilising tens of thousands of troops from both sides, as well as some member states of the UN Command.
South Korean lawmakers have said the North could seek to fire an intercontinental ballistic missile or take other military action to protest the allies' drills or last week's summit of South Korea, the United States and Japan.
