The National Health Insurance Service said the suit, filed in Seoul's district court, named Phillip Morris, British American Tobacco (BAT) and South Korea's largest tobacco firm KT and G.
"Smoking is a serious issue affecting people, particularly the youth and women," the agency said in a statement.
"So we will push ahead with this suit with a strong determination, for the future of our nation and the sustainability of our health insurance."
The damages figure was calculated from the agency's spending on patients who smoked for more than 30 years before being diagnosed with one of three types of cancer most likely to be caused by smoking.
The cancers are two types of lung cancers and a type of throat cancer, the insurer said.
The move came days after the Supreme Court rejected a damages suit filed by 30 lung cancer patients against KT and G.
The court ruled that it was "difficult" to prove a causal relation between smoking and lung cancer based solely on the fact that certain smokers developed the disease.
Around 25 percent of South Korean adults are smokers, with the figure for male adults standing at 43.3 percent and 10 percent for teenagers.