Anna was the daughter of Count Henry of Stolberg (1509–1572) and his wife, Elisabeth of Gleichen (died 1578).

Anna III was elected to succeed Elisabeth II, Abbess of Quedlinburg.

The election of the new princess-abbess was confirmed by Holy Roman Emperor Rudolf II.

The Princess-Abbess selected Anne Margaret of Brunswick-Harburg as her coadjutrix but the Duke of Saxe-Weimar refused to consent as he wanted his own sister, Maria, to succeed Anna III.

Anna III died suddenly aged 36 after a walk.