The HC Andersen Literature Award was presented by Danish Crown Princess Mary at the Concert Hall of Odense, which is Denmark's third largest city and the hometown to Andersen.
Rushdie also received 500,000 Danish kroner (some 90,000 dollars) and a statue of "Ugly Duckling", created by Danish sculptor Stine Ring Hansen.
According to the literature award's committee, Rushdie received the award "due to the fact that he is an incomparable author, who through a blend of global realism and fairytale fantasy depicts the significance of journeys and cultural meetings for our time, and thus enriches world literature".
Rushdie said Andersen's work had always fascinated him and stimulated his own imagination both as a young reader and as an adult.
Established in 2010, the HC Andersen Literature Award is a Danish international literary prize to celebrate Andersen's influence on writers throughout the world.
Previous winners include Brazilian novelist Paulo Coelho, J.K. Rowling and Chilean born writer Isabel Allende.
Located some 160 km west of Copenhagen on Denmark's second largest island of Funen, Odense is hometown to Andersen, who left for Copenhagen at 14 to seek employment there.