Her father, Mihail Schapira, was a successful businessman and financial advisor to King Carol II of Romania. Sonnabend was, for many years, married to Leo Castelli, whom she met in Bucharest in 1932 and married soon after. The couple had a daughter, Nina Sundell. She and her husband left Europe during the 1940s and settled in New York City. During the 1940s her mother Marianne Schapira divorced her father and met and married the Russian-born American painter John D. Graham (who was a mentor figure to artists such as Jackson Pollock, Willem de Kooning, and Arshile Gorky). Graham also became a mentor to Ileana and Leo by introducing them to his artist friends in the New York art world. In 1950, the couple curated a show of young American and European painters which included both Jean Dubuffet and Mark Rothko. After divorcing Castelli (with whom she remained lifelong friends) in 1959 she married Polish-born Michelangelo scholar Michael Sonnabend whom she had met during the 1940s.