For South Korea, the U.S. Department of State issued a "Do Not Travel" advisory for the city of Daegu "due to the level of community transmission of the virus and imposition of local quarantine procedures."
On March 4, Korean Air said it would reduce its flights between Seoul and Atlanta from daily to four times a week through April 25. The carrier is also suspending or reducing other routes around the world.
People coming to the United States from Italy and South Korea are also now being screened.
Delta is also allowing passengers with bookings to Seoul to change their travel plans without paying a change fee.
Along with the reduction of flights from the United States to Seoul, the airline also said it will delay the start of planned new flights from Seoul's Incheon airport to Manila until May 1.
Delta is allowing passengers whose flights are affected to request a refund, be rebooked on Delta or Delta partner flights or on flights after April 30, or discuss other options.
Korean Air, a joint-venture partner of Delta's, also flies from Atlanta to Seoul.
Delta said it has put in place a number of processes and mitigation strategies to respond to the growing concern about the spreading illness. It is in contact with communicable disease experts at the CDC, World Health Organization and local health officials to ensure its training, procedures and cabin cleaning and disinfection measures meet or exceed guidelines.
The reduction of flights to Korea comes after Delta and other U.S. airlines suspended flights to China.
The International Air Transport Association, a global airline group, said last week it estimates global airline traffic could be reduced by 4.7% by the virus, which would be the first overall decline in demand since 2009.
That could translate into $29.3 billion in lost passenger revenues for airlines worldwide, according to IATA.
Delta's stock has dropped more than 11 percent so far this week.