The fixture will be played in Austria on November 14 at a yet-to-be confirmed venue, the Mexican Football Federation said in a statement, reports Xinhua news agency.
Mexico have won seven and drawn two of their 13 previous meetings with South Korea.
Gerardo Martino's men are among five teams that have already qualified for the last phase of 2022 World Cup qualifiers in the North American, Central American and Caribbean (CONCACAF) region. The others are the United States, Costa Rica, Jamaica and Honduras.
The 2021 Gold Cup - the CONCACAF region's premier international competition - will be played from July 10 to August 1.
Mexico beat the Netherlands 1-0 in a friendly in Amsterdam last week and face Algeria in the Hague on Tuesday.