She is the first recipient of the 500,000 kroner ($93,352) award, which was handed out Tuesday at a ceremony in Odense, Andersen's hometown.
The prize is given to a person who can be compared with Andersen, the Danish writer who was born in 1805 and wrote some 160 fairy tales and poems before his death in 1875.
Rowling said the author of such classics as "The Little Mermaid" and the "The Ugly Duckling" had "created indestructible, eternal characters."
Rowling's seven books about the boy wizard have sold more than 400 million copies worldwide and have been translated into many languages.
