Alonso's dance studies began in her childhood with flamenco lessons in Spain. Later she studied ballet in Havana and then, at age 17, enrolled in the School of American Ballet in New York City. Having made her stage debut in the musical comedy Great Lady in 1938, she joined George Balanchine's Ballet Caravan in 1939 but moved to the newly formed Ballet Theatre (later American Ballet Theatre) in 1940; after one year she was forced to leave because of eye problems (a difficulty that persisted throughout her life). Alonso returned to Ballet Theatre in 1943 and danced the lead in Giselle, remaining with the company for five years. She then began to tour as a guest dancer, often with partner Igor Youskevitch, and in 1948 founded the Alicia Alonso Ballet Company in Cuba, through which she became known for her artistry as a choreographer, which ranged from variations on classic works such as Swan Lake to the comic ballet A Voyage to the Moon.

Over the next 14 years Alonso danced with many companies, including the Ballet Russe de Monte Carlo from 1955 to 1959. Her own company was renamed Ballet de Cuba in 1955. In 1957 she became the first Western dancer invited to perform in the Soviet Union. After Fidel Castro came into power in Cuba in 1959, her ballet company was renamed Ballet Nacional de Cuba (National Ballet of Cuba), with Alonso remaining as its director. UNESCO awarded her the Pablo Picasso Medal, its award for notable contributions to arts or culture, in 1999.