According to the outlet, a Cheongung medium-range surface-to-air missile exploded at around 10:38 a.m. local time (01:38 GMT) some 53 miles northeast of Seoul.
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The missile is designed to explode in cases of guidance system failures after launch, the air force's official explained.
The accident caused no casualties or material damage, and a task force has been formed to investigate the cause of the accident, he added.
The Cheongung (KM-SAM) missile, which was designed by South Korea with Russia's technical support, was first tested in a live-firing mission late 2017. The 15-foot-long missile is capable of striking an aircraft at a range of 25 miles and an altitude of up to 10 miles.