Born on 23 July 1841 in Vammen to the north-west of Viborg, Zahrtmann was the daughter of Johan Henrich Zahrtmann and his wife Marie Dorothea Poulsen.
In 1855, while her sister was undergoing an operation at Frederiks Hospital in Copenhagen, Søren Kirkegaard died at the hospital, awakening Zahrtmann's interest in the philosopher.