Ms Kim's warning came in response to South Korea's defence chief Suh Wook who said that the military had advanced weapons capable of "accurately and quickly" hitting "any target" in North Korea.
Ms Kim called Mr Suh a "lunatic" and said mentioning a pre-emptive strike against a nuclear power was a "very big mistake", state news agency KCNA said.
As South Korea's new president Yoon Suk-yeol prepares for his new term in May, members of his team have made public show-of-force statements against the North.
Mr Yoon's transition team on Tuesday again did not rule out the option of launching a pre-emptive strike if necessary.
"Pre-emptive strikes are one of the actions that are accepted globally, including at the UN, as a viable option ... when a pre-emptive threat persists," Mr Yoon's spokeswoman Kim Eun-hye told reporters on Tuesday.
The exchange comes as North Korea has resumed its sanctions-breaking weapons tests with an unprecedented blitz this year, last month firing its first intercontinental ballistic missile at full range since 2017.
"In case South Korea opts for military confrontation with us, our nuclear combat force will have to inevitably carry out its duty," said Kim Yo Jong, who is a leading policy adviser in Pyongyang.
She said the "primary mission" for her country's nuclear forces was to act as a deterrent but if an armed conflict was to break out, such weapons would be used for "eliminating the enemy's armed forces at a strike".
Ms Kim earlier had warned the South to "discipline itself if it wants to stave off disaster".
North Korea had paused its long-range and nuclear tests when Kim Jong-un and then-US president Donald Trump engaged in a high-profile bout of diplomacy that subsequently collapsed in 2019. Talks have since stalled.
For five years under President Moon Jae-in, Seoul has pursued a policy of engagement with Pyongyang, including brokering high-level summits between Mr Kim and Mr Trump while reducing joint US military drills that the North regards as provocative.
But Mr Yoon, who will take office next month, says this "subservient" approach has been a failure. He has promised to take a hard line on Pyongyang.
North Korea will this month mark the 110th anniversary of the birth of founder Kim Il Sung, the grandfather of current leader Kim.