Moro studied medicine in Graz, Austria, getting his M.D. in 1899. From 1901 to 1902 he worked with Theodor Escherich (1857-1911) in Vienna, the discoverer of the Escherichia coli bacterium. He was habilitated for pediatrics in Munich in 1906, and became a professor of pediatrics in the University of Heidelberg in 1911.
Besides the Moro reflex he became also known for the following:
In 1936, after the Nazis came to power, Moro resigned from his chair at the University of Heidelberg, alleging reasons of health. However the real motive is that he was married to Grete Moro, née Königsvald, of Jewish origin. He started a private clinic at Mozartstrasse 10 (where a commemorative plaque is now affixed) and retired in 1948.