Her father, Captain Johan Adolph Fibiger, was an army officer; her mother was Margrethe Cecilia Nielsen Aasen.

It is a partial autobiographical story of a young woman, Clara Raphael, who works as a governess in the provinces; it is based in part on Fibiger's experiences as a private tutor on the island of Lolland in 1849.

[2] In counter opinions in society against women's rights, Fibiger published two pamphlets; Hvad er Emancipation?

Her later novels included En Skizze efter det virkelige Liv (A Sketch from Real Life, 1853) and Minona.

Such was her prominence as an advocate for gender equality, in order to honour it, the Dansk Kvindesamfund (Danish Women's Society) created Mathildeprisen (The Mathilde Prize).

A small garden square adjacent to the Women's Museum in central Aarhus is also named "Mathilde Fibigers Have" in her honor.

Kvindernes Boligforening's building at Østerbrogade 85 in Copenhagen is named Clara Raphaels Hus in honor of Fibiger.