The metropolitan health department culled about 16,000 ducks at the farm and three other nearby farms in the city some 330 km south of the capital, WAM news agency reported Sunday.
While the H7 strain is not highly contagious for humans, there is a possibility that it could mutate into a more virulent form.
Officials have banned all transportation of duck-related products until quarantine officials conclude an epidemiological investigation of a farm suspected to be the source of the outbreak.
The country had been hit by the bird flu epidemic twice, once in the winter of 2003 and the next time in 2006. During the last outbreak, Seoul spent about $63.4 million to compensate farmers.
Nine million ducks and 70 million chickens are farmed domestically in South Korea.