The military "urgently deployed its powerful forces to all pharmacies in Pyongyang City and began to supply medicines under the 24-hour service system", KCNA said.
One KCNA photo showed soldiers walking next to a long line of green trucks.
Kim had strongly criticised healthcare officials for their failure to keep pharmacies open.
North Korea's leader has put himself front and centre of the country's Covid response since its first case was announced last week, saying the outbreak is causing "great upheaval".
Authorities had reported more than 1.48 million cases of "fever" as of Monday evening, KCNA said, with the death toll at 56.
"At least 663,910 are under medical treatment," the agency said.
Authorities have stepped up media awareness campaigns and pharmaceutical factories have increased the production of medicines, KCNA reported.
No response to South Korea
North Korea has one of the world's worst healthcare systems, with poorly-equipped hospitals, few intensive care units, and no Covid treatment drugs or mass testing ability, experts say.
"Most North Koreans are chronically malnourished and unvaccinated, there are barely any medicines left in the country, and the health infrastructure is incapable to deal with this pandemic," Lina Yoon, senior Korea researcher at Human Rights Watch, said in a statement.
She urged the international community to offer medicines, vaccines and infrastructure to North Korea.
Pyongyang has so far not responded to an offer of help from Seoul, according to South Korea's unification ministry.
South Korea's new president Yoon Suk-yeol has taken a hawkish stance on his country's nuclear-armed neighbour, but told lawmakers Monday that he would "not hold back" on aid -- if Pyongyang accepts.
Despite the Covid crisis, new satellite imagery has indicated North Korea has resumed construction at a long-dormant nuclear reactor.
The United States and South Korea have warned that Kim is preparing to conduct another nuclear test -- the country's seventh.