Lindström is the only child born to Ingrid Bergman and her first husband, Swedish neurosurgeon Petter Lindström. She was greatly affected by her mother's abandonment when her mother left her father for Italian director Roberto Rossellini. Petter Lindström sued for desertion and waged a custody battle with Bergman for their daughter, and Pia did not reunite with her mother until 1957. Her half-brother, Roberto Ingmar Rossellini, was born on 7 February 1950, and her mother married Roberto Rossellini on 24 May 1950. On 18 June 1952, Lindström's twin half-sisters Isabella Rossellini and Isotta Rossellini were born.