Some Asian countries have a tradition of eating dog
Fifa President Sepp Blatter said the issue was harming the country's international image ahead of next year's World Cup, which South Korea is co-hosting with Japan.
He said he was making the appeal after receiving thousands of letters from members of the public.
South Korea banned dog restaurants during the 1988 Seoul Olympics, but spicy dog soup is still very popular in summertime, especially among older men.
The meat is widely considered to improve strength and virility.
Under methods now officially banned, dogs used to be hanged or beaten with bats to soften the flesh before slaughter. But Fifa said dogs were still being tortured, despite laws banning the mistreatment of animals.
Unhygienic conditions
Mr Blatter wrote to Fifa vice president Dr Chung Mong-Joon, who is president of South Korea's football association and a member of parliament, urging him to "take immediate and decisive measures to put an immediate end to this cruelty".
"The World Cup would serve as an appropriate moment for Korea to show the world that it is sensitive to vociferous worldwide public opinion and that it rejects cruelty," Mr Blatter said in a statement.
Mr Blatter said he had received assurances from Dr Chung that a government investigation would make sure the law was enforced.
In South Korea, dogs are still raised specifically for eating. They are kept in unhygienic conditions in crowded cages, and tend to be killed by electric shock.
Fifa is hoping the government will bring in the same law it used in 1988 to stop the sale of dog meat, said spokesman Andreas Herren. It also wants South Korea to stop cruelty to cats.
"We really got thousands of e-mails and letters, especially from Britain and the United States," said Mr Herren. "Animal rights have been an issue for two or three years and picked up strongly in the past two or three months."
South Korea and Japan are hosting the 64-match World Cup finals from 31 May to 30 June next year.