The price of U.S. cheese has jumped to a record high thanks in part to an appetite for pizza and junk food from emerging markets like South Korea.

Koreans have developed a taste for cheese, particularly on pizzas, turning the country into the second-biggest importer of cheese from the U.S. after Mexico. The Asian nation imported 49,000 metric tons in 2013, 25% more than the previous year, according to data from the U.S. Dairy Export Council. In dollar terms, U.S. cheese exports to South Korea rose to $348 million last year...