The 61-year-old man, identified only by his surname Kim, broke into the education ministry office and threw a petrol bomb, a fire brigade spokesman in the capital told AFP, adding that ministry staff managed to put out the fire.
The man, who Yonhap news agency said was believed to be a maintenance worker at the building, was taken to hospital but pronounced dead soon afterwards.
The fire brigade spokesman said the fire had damaged a few chairs, desks and documents, adding that an investigation was under way.
South Korea has one of the world’s highest suicide rates. Government data showed the nation’s 2009 suicide rate was 33.8 people per 100,000 – the highest among members of the Organization for Economic Cooperation and Development.