Born in Ostritz, Lausitz, the son of the rector of the municipal school, Kretschmer received first musical instruction from his father.
From 1846, he studied in Dresden, composition with Ernst Julius Otto and organ with Johann Gottlieb Schneider.
In 1863, he was appointed Hoforganist (Court Organist) and instructor of the Kapellknabeninstitut, and in 1880 also choral conductor of the Hofkirche.
His composition Die Geisterschlacht won a prize at the first Deutsches Sängerfest in 1865.
He then composed his first opera, Die Folkunger, from a libretto by Salomon Hermann Mosenthal.