Heinze was born on 11 August 1867 in Naumburg, Province of Saxony, Kingdom of Prussia.
He studied classical philology at the University of Leipzig under Otto Ribbeck (1827–1898), later relocating to the University of Bonn (1887), where he had as instructors, Hermann Usener (1834–1905) and Franz Bücheler (1837–1908).
Afterwards, he studied in Berlin with Theodor Mommsen (1817–1903), earning his habilitation in 1893 at the University of Strasbourg with a treatise on the philosopher Xenocrates.
In 1923, he succeeded Georg Wissowa (1859–1931) as editor of the magazine Hermes.
Richard Heinze is remembered for his expert analysis of ancient authors that included Ovid, Lucretius and Virgil.