The St. Petersburg-born dancer was trained in Paris and London. She first came to notice in 1936 with Les Ballets de Monte-Carlo, where Fokine coached her through his own works. The Ballet Russe de Monte Carlo, which grew out of that company, was founded in 1938, with Krassovska as one of its principal dancers.

From 1950 to 1955 she danced with the London Festival Ballet. In 1963, she movedoved to Dallas, where she opened a ballet school with its own student company, the Krassovska Ballet Jeunesse.