He was born in the then Ratibor, Province of Silesia, son of Felix Mendelssohn's second cousin Wilhelm Mendelssohn (1821–1866) who had married in 1854 Louise Aimee Cauer (sister to Bertha Cauer). Arnold Ludwig himself married in 1885 his second cousin Maria Cauer, daughter of Carl Cauer (brother of Ludwig Cauer).
Mendelssohn was originally a lawyer before studying music, then was director of church music and a professor in Darmstadt. Paul Hindemith was one of his students. After his death his works were banned in Nazi Germany because of his Jewish heritage.
^Françoise Tillard Fanny Mendelssohn 1996 "The composer Arnold Mendelssohn (1855-1933), nephew of the doctor and son of his brother Wilhelm (1855-1933), once observed: "The Mendelssohn family's attitude to Uncle Arnold and Aunt Dorothea is typically Jewish: nobody must think of them."