Kim thanked what was referred to as a research group for the system.
The test-firing on Thursday showed it was "highly reliable" and its combat response was "advantageous", KCNA said in its report.
The test conducted by North Korea's Missile Administration was to examine the performance of a system whose production had already begun, it said on Friday.
KCNA did not specify where the test was held, but said Kim was joined by members of the Central Military Commission of the ruling Workers' Party of Korea.
Photographs supplied by KCNA showed a plume from a missile soaring into the sky and a midair explosion.
Other images showed Kim apparently observing the test and then smiling.
Experts said Pyongyang might be receiving help from Russia for the anti-aircraft missile system, particularly given how security ties have become increasingly entwined.
"In the past North Korea has introduced Soviet weapon systems and developed weapons based on them, and it is highly likely that Russia has given correspondingly what North Korea demands because of the strengthening of co-operation," said Shin Seung-ki, head of research on North Korea's military at the state-run Korea Institute for Defence Analyses.
South Korea's national security adviser said in 2024 that Russia had provided North Korea with anti-air missiles and air defence equipment in return for sending troops to support Moscow in its war against Ukraine.
Shin also noted although North Korea has made ballistic missiles on its own, it was far harder to produce interceptor missiles without additional help.
"It's much more complicated because there's not just missiles, but a detection and tracking radar, and there's a command and control system," Shin said.
South Korea's military was aware in advance of a possible missile launch, Yonhap News Agency reported, citing an official from the Joint Chiefs of Staff.
Seoul and Washington wrapped up their latest annual joint military drills, known as Freedom Shield, on Thursday.
They say such exercises are defensive, but Pyongyang has long demanded a halt to US-South Korea joint exercises, branding them a prelude to an invasion.
In a statement carried by KCNA, North Korea's defence ministry criticised the latest joint drills by South Korea and the United States, calling them "reckless" and "a rehearsal of war".
All options for containing the US and South Korea were being considered, including the use of the "most destructive and deadly military means", the statement said, while urging the militaries of both countries to stop their acts.
