Elisabeth's mother Maria Anna was a daughter of Leopold IV, Duke of Anhalt and Princess Frederica of Prussia, Duchess of Anhalt-Dessau.

Her siblings included Marie, Princess of Saxe-Altenburg, Louise Margaret, Duchess of Connaught and Strathearn, and Prince Friedrich Leopold of Prussia.

On 18 February 1878, Elisabeth Anna married Frederick Augustus, Hereditary Grand Duke of Oldenburg.

Due to this increased status, the weddings were attended by many important personages, including King Leopold II of the Belgians and his wife Queen Marie Henriette.

Her husband later married Elisabeth Alexandrine of Mecklenburg-Schwerin, daughter of Frederick Francis II, Grand Duke of Mecklenburg.