[1][3] She was the daughter of opera singers Franz Mejo and Rosa Mejo-Straub, one of their seven children, all of whom had stage careers.
[1] She began her career on the stage as a child;[1] making her first appearance at a very young age in Breslau in a production of Der Rattenfänger von Hameln (English: Pied Piper of Hamelin) that was directed by her father.
Her singing in this production drew the attention of the Berlin theatre director Carl who subsequently had Grobecker trained as a soubrette.
[4] Anna Grobecker was the first operetta singer to be invited to perform for the Imperial Court in Vienna, in 1861.
[4] In 1865, she made a guest appearance at the Meysels-Theater, Berlin, creating the trousers part of Ganymed in Suppe's Die schöne Galathée.