The message warning of a 6.5-magnitude quake was part of a five-day disaster response exercise and should never have been faxed.
International media including China's official Xinhua news agency ran the warning before the Korea Meteorological Administration issued a red-faced apology.
"We apologise deeply for causing inconvenience," the KMA said in a statement quoted by South Korean news agency Yonhap, which also carried the initial alert.
"The message was made for an exercise purpose, and an employee mistakenly clicked the button to send the message."
Strong quakes are very rare on the Korean peninsula. Some seismological disturbances recorded in the South have been attributed to North Korean nuclear tests across the border.