"If the enemy persists in such dangerous actions as provoking the entry of the virus into our republic, we will respond to this not only by destroying the virus, but also by destroying the South Korean authorities," Yonhap news agency quoted her as saying.
"We have already considered various counteraction plans but our countermeasure must be a deadly retaliatory one."
Jong further issued blame on "South Korean puppets" for sending "dirty objects" into North Korea's borders, in likely reference to the pamphlets often sent over the DMZ line.
The North Korean leader's sister also revealed that her brother had suffered from a "fever" and had been "seriously ill," but that he could "not lie down for even a moment because of his concerns of the people."
It was not specified whether Kim Jong Un was suffering from what North Korea has been documenting as "fever cases."
Earlier Thursday, Kim Jong Un announced the victory over the coronavirus outbreak in North Korea - three months after the first outbreak was reported.