MERS is caused by a coronavirus from the same family as the one that caused SARS.
The World Health Organization (WHO) has not recommended travel restrictions and its director-general, Margaret Chan, said she believed South Korea would be able to control the spread.
But alarm is growing and about 25,000 people cancelled trips to South Korea between June 5 and June 7, the Korean Tourism Organization said.
Hong Kong raised its response level to "serious", from "alert" on its three-level system. The third is "emergency".