Father:
Friedrich Wilhelm I, King of Prussia (1688-1740)
Mother:
Sophie Dorothea of Hanover (1687–1757)

Spouse:
Friedrich von der Trenck (1723-1794)

She was a younger sister of Wilhelmine, Margravine of Bayreuth, Frederick II, King of Prussia and Louise Ulrika, Queen of Sweden and Augustus William, Prince of Prussia.

Born in Berlin, she was eleven years younger than her brother, and would have been seven years old when he made his abortive attempt to run away from home, after being humiliated by his father.

Both children were musically inclined, but for Anna formal musical instruction was only possible after the death of her music-hating father. Music was her secret consolation against his cruelty to her (he would often drag her across a room by the hair during his rages).

Anna learned to play the harpsichord, flute, and violin, receiving her first lessons from her brother, which her more 'civilised' mother encouraged.

In 1743*, Anna secretly married Baron Friedrich von der Trenck, a man whose adventures inspired works by literary greats such as Victor Hugo and Voltaire. When her brother, who had ascended to the throne in 1740, discovered she had married and was pregnant, he packed her off in a rage to Quedlinburg Abbey, a place where many aristocratic women were sent to give birth to children out of wedlock. Anna's marriage was annulled at the request of Friedrich II, and von der Trenck was imprisoned for ten years. However, Anna continued to correspond with him until her death.

Anna became the Abbess of Quedlinburg in 1755, making her a wealthy woman. She chose to spend most of her time in Berlin, where she devoted herself to music, and became known as a musical patron and composer.

In 1758, Anna began a serious study of musical theory and composition, engaging as her tutor Johann Philipp Kirnberger, a student of Johann Sebastian Bach. She composed chamber music, such as flute sonatas, and wrote music to Ramler's Passion cantata ("The Death of Jesus"); this was also her favorite piece. Only a few of her works have survived, and it is probable that she may have destroyed many of her compositions. After all, she did describe herself as being very "timorous and self-critical."

Anna was also a collector of old music, preserving over 600 volumes of works by notables such as Johann Sebastian Bach, George Frideric Handel, George Philipp Telemann, and others. This act in itself was a significant contribution to Western culture. Her library was split between East Germany and West Germany after World War II, and despite serious depredations by fire in 2004, still survives today.