Anna Elisabeth Louise was one of five children born to Margrave Frederick William of Brandenburg-Schwedt and Sophia Dorothea of Prussia.

On 27 September 1755 in Charlottenburg Palace, Berlin, Anna Elisabeth Louise married her uncle Prince Augustus Ferdinand of Prussia, a younger brother of her mother, Sophia Dorothea.

He was eight years older than she and was a younger son of Frederick William I of Prussia and Sophia Dorothea of Hanover (herself the only daughter of George I of Great Britain).

While most of the royal family left, reportedly because of the anti-Napoleonic criticism they had expressed, and the members of the royal court either followed them or left the capital for their country estates, Elisabeth Louise remained with her spouse and Princess Wilhelmina of Hesse-Kassel because of "their great age", as did Princess Augusta of Prussia, who was pregnant at the time.

On 27 September 1755 in Charlottenburg Palace, Berlin, Anna Elisabeth Louise married her uncle Prince Augustus Ferdinand of Prussia The couple had seven children: