Rose of Lima Parochial School in Brooklyn until the third grade. When Moore was eight years old, the family relocated to Los Angeles, California at the recommendation of her uncle, an employee of MCA. Moore's paternal great-grandfather, Lieutenant Colonel Lewis Tilghman Moore, owned the house which is now the Stonewall Jackson's Headquarters Museum in Winchester, Virginia.
Moore was the oldest of three children with a younger brother John and a younger sister Elizabeth. The Moores later lived in a rented apartment at 144-16 35th Avenue in Flushing, Queens, New York City. Her Irish-Catholic family lived in Brooklyn's Flatbush neighborhood.
Moore was born on December 29, 1936, in the Brooklyn Heights neighborhood in Brooklyn, New York City, New York, to Marjorie (née Hackett) and George Tyler Moore.