Shields was born in New York City, the eldest son of Francis Xavier Alexander Sr. (1909–1975), a top-ranking American tennis player, and Italian Princess Donna Marina Torlonia di Civitella-Cesi (1916–1960). His mother's family is descended from several Italian princely families (most notably Borgia, Medici, d'Este, di Savoia). Shields' uncle was Don Alessandro Torlonia, 5th Prince di Civitella-Cesi, the husband of the Spanish Infanta Beatriz de Borbón y Battenberg, meaning Shields and King Juan Carlos of Spain share cousins in the Torlonia-de Borbón family. Together, his parents had two children: (1) Francis Alexander, and (2) Marina Shields (born 1943).