The queen of Italian dance would have turned 85 in August.
"With her elegance and her artistic efforts, the fruit of intense work, Carla Fracci honoured our country," said President Sergio Mattarella.
"I express my most deep-felt condolences to her family and to the world of dance, which has lost a precious and unforgettable figure today.
"Her extraordinary artistic and human qualities made her one of the greatest ballet dancers of our time at the international level". Fracci was born in Milan in 1936 and started out at the La Scala Theatre Ballet School at the age of 10, having Russian dancer Vera Volkova among her teachers.