The launch on Sunday was overseen by leader Kim Jong-un, who praised progress in strengthening the country's war readiness, state media reported on Tuesday.
Kim said the test, conducted by North Korea's Missile Administration, demonstrated a significant development in the country's armed forces' ability to fight and "the enemy will know better what such progress means without any explanation".
"He affirmed that such reality would give the enemy an incurable headache and a very cruel and unavoidable blow," Kim was cited as saying.
The KCNA report did not specify the type of weapon tested.
Photographs released by KCNA showed Kim, accompanied by his teenage daughter, inspecting a screen displaying a map of the country's east coast and the "flight trajectory" of Hwasongpho-11-ma-1, which is likely part of a series of short-range ballistic missiles being upgraded by Pyongyang.
NK News, a Seoul-based website specialising in North Korea, said the projectile appeared to be an upgraded variant of a missile equipped with a hypersonic glide vehicle.
Mounting a glide vehicle on a missile means the warhead can manoeuvre to evade anti-missile defences and also potentially be launched partially into orbit.
Hypersonic missiles are among a range of weapons that Kim has called for development to upgrade its nuclear capabilities.
The South Korean military said on Sunday that North Korea fired two short-range ballistic missiles off its east coast.
The test came days after Pyongyang accused the US of raising tensions on the Korean Peninsula through a series of military drills.
On Monday, the foreign ministers of South Korea, Japan and the United States met on the sidelines of the UN General Assembly in New York to agree to co-ordinate closely for peace, stability and denuclearisation on the Korean Peninsula, according to Seoul's foreign ministry.
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