Korea’s cash rule turns on USD 10,000. Which version applies depends on whether you are entering or leaving, and on who you are.
Bringing money in
Up to USD 10,000 needs nothing: “If you bring in means of payment not exceeding USD 10,000 to Korea, you do not need any permission or declaration.” Above it, the Korea Customs Service says: “if you enter the country with foreign currency, KRW notes, or checks above USD 10,000 or the equivalent in total, you must report it to the Customs. The same goes for cashier’s checks in Korean won.”
Taking money out
Residents and non-residents alike: “If Korean residents or non-residents carry means of payment (means of international payment, KRW notes, or cashier’s checks) less than USD 10,000 out of Korea, no report is required.”
Above that amount, the published rule is addressed to Korean nationals: “if a resident of Korean nationality transports means of payment (means of international payment, KRW notes, or cashier’s checks) that exceeds USD 10,000 for general overseas travel expenses, he or she can take it with him or her if he or she reports it to the head of the competent Customs office.”
That rule does not describe a departing visitor, so a visitor carrying more than the threshold is relying on a rule written for someone else. Leaving with less avoids the question, and you can send the balance ahead instead of carrying it.
Relocation, study and travel-agency money
Some travellers need a bank confirmation instead of a customs declaration:
If overseas Koreans, Korean expatriates, overseas students, and travel agents carry overseas travel expenses exceeding USD 10,000, or if a foreign resident intends to leave the country with earned income in Korea, he/she must obtain confirmation from the head of the foreign exchange bank (in this case, there is no separate customs declaration, but a certificate of confirmation must be presented at the request by the Customs office).
That list does not cover every departing traveller over the threshold.
How to report
Per the source: “Mark yes on no. 3 of Traveler Declaration Form with entering specific amount, submit it to Customs official, and receive The Certificate of Foreign Currency Declaration.”
Do this before you leave the immigration area. The source is explicit: “The Certificate of Foreign Currency Declaration cannot be issued after entering Korea (after leaving the immigration).”
The penalty for not reporting
The source states it without qualification:
Any person who export or import any means of payment including foreign currency without filing a report shall be punished by imprisonment with labor not more than 1 year or by a fine (Article 32 of the Act) not exceeding one hundred million won
That is a criminal penalty for missing a form.
If you are near the threshold
Arrive without the cash. Money sent ahead with Wise and drawn locally never crosses the border in a bag, so neither rule reaches it.
What the page does not say
The rules cover Korean nationals leaving with more than the threshold (a Customs report) and a defined set of people leaving with Korea-earned income or relocation funds (a bank confirmation). Korea Customs’ page does not say which applies to an ordinary non-Korean tourist leaving with more than USD 10,000 that is not Korean-earned income. If that is you, confirm with Korea Customs before you fly.
Send it ahead instead of declaring it at the counter (affiliate link)