Born in Belgrade, Ćurčić moved to Copenhagen at the age of one with her family where her father worked at the Yugoslavian embassy. Danica Curcic attended Sankt Annæ Gymnasium before obtaining a bachelor's degree in film and media studies from the University of Copenhagen. She then spent a year in California where she took acting classes at the Dell'Arte International School of Physical Theatre before enrolling at the Danish National School of Performing Arts, graduating in 2012.
