Born in Aarhus, Denmark, Schytte originally trained as a pharmacist. He studied with Niels Gade and Edmund Neupert. In 1884, he travelled to Germany to study with Franz Liszt. Schytte lived and taught in Vienna between 1886 and 1907 and spent the last two years of his life teaching in Berlin.
Schytte composed a Piano Concerto in C-sharp minor, Op. 28, and a Sonata in B-flat, among numerous other piano works. He also wrote two operas: Hero (25 September 1898 in Copenhagen) and Der Mameluk (22 December 1903 in Vienna). His shorter works are still used today as educational studies for piano students.
- School of modern pianoforte virtuosity (Schule des höheren Klavierspiels: technische Studien bis zur höchsten Ausbildung). Edited by Moriz Rosenthal and Ludvig Schytte. Berlin, ca. 1890.
- Die Schule des modernen Klavierspiels ... School of Modern Pianoforte Playing. A Collection of Studies as Introduction to Modern Harmony, Melody, Rhythm and Style. Op. 174, etc. London: A. Lengnick & Co, 1912.