Lee Jong-joo, a spokeswoman for the South's nine-member economic delegation, had said Seoul would have a "strong response" if the North's government did more than warn, fine or expel the worker.
Relations between the two countries have been especially tense since the North's launch of a rocket earlier this month and its subsequent decision to expel nuclear inspectors and restart its nuclear activities following a rebuke from the UN Security Council.
South Korean firms benefit from cheap North Korean labour and land at Kaesong, while the cash-strapped North receives a steady flow of foreign currency in return.
Relations between the two countries had worsened since Lee Myung-bak became South Korea's president in February 2008.
In December, Pyongyang restricted border crossings and expelled hundreds of South Korean managers from the industrial park, which was once hailed as a model for economic co-operation between the neighbours.
This was in response to Seoul's decision to cut aid to the North in an effort to push it towards denuclearisation.
Officials have released few details about Tuesday's talks, but in a sign of the possible tensions surrounding them, South Korea's unification ministry said the two sides had trouble deciding on a venue or format for the discussions.
North Korea launched a rocket on April 5, which critics say was a disguised long-range missile test that violated UN resolutions.
The UN Security Council condemned Pyongyang for the launch and called for tighter enforcement of existing sanctions.
In response, Pyongyang said it would boycott six-nation nuclear disarmament talks, restart its nuclear facilities and threatened war with the South if it joined a US-backed initiative to halt the proliferation of illicit weapons.