President Miguel Diaz-Canel said: "Alicia Alonso has gone and left an enormous void but unbeatable legacy.
"She positioned Cuba at the altar of the best of dance worldwide. Thank you Alicia for your immortal work."
Alonso was born Alicia Ernestina de la Caridad Martinez del Hoyo on 21 December 1921. She first appeared on stage at the age of 10, and fell in love with ballet.
"When you look out and you see the theatre full of people, you feel that you are alive, that you have been born," she told the BBC in 2015. "It's wonderful, it's unique."
She married fellow student Fernando Alonso when she was 16, and the couple moved to New York to join Ballet Caravan.
Considered one of the 20th century's greatest ballerinas, Alonso began to lose her sight aged 19, and relied upon the stage lights to guide her.
When she eventually went for tests, she was diagnosed with severe retinal detachment. Over the following two years she underwent three major eye operations that involved long periods of recovery where teachers would come to her bedside to teach her the steps, moving her fingers to help her decipher the moves.
She enjoyed major roles in the Forties, including star turns as Giselle in New York and London. In 1948 she founded the Alicia Alonso Ballet COmpany in Cuba's capital – it collapsed in 1956 due to lack of financing.
After the revolution, she reportedly received help from Fidel Castro to form the National Ballet of Cuba. According to her 1981 biography, she told him she needed $100,000.
"We will give you $200,0000," he replied.
Alonso continued to direct the ballet company and dance until her seventies.
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