The celebrity gossip magazine printed pictures of the duchess taken during the couple's private holiday in France.
A royal spokesman said the legal proceedings had been launched in France and were for breach of privacy.
Closer's editor said the couple were "visible from the street".
"These photos are not in the least shocking. They show a young woman sunbathing topless, like the millions of women you see on beaches," said Laurence Pieau.
She described the reaction as "a little disproportionate".
