Danner was born in Philadelphia, Pennsylvania. She is the daughter of Katharine (née Kile) and Harry Earl Danner, a bank executive. She has a brother, opera singer/actor Harry Danner, a sister, performer-turned-director Dorothy (Dottie) Danner, and a half-brother, violin maker William Moennig. Danner is of part Pennsylvania Dutch ancestry, and one of her great-grandmothers was born in Barbados (a White Barbadian).