Alfred Arnstein was born in Vienna on 26 June 1886 as the son of the lawyer Emanuel Arnstein and Regina Hahn. He married Hildegard Arnstein, née Baum, in 1920. After completing a doctorate in medicine at the University of Vienna in 1910, he was appointed deputy assistant doctor (Assistenzarztstellvertreter) in the 3rd Medical Clinic (Wilhelm Schlesinger department) at the General Hospital (AKH) in Vienna in September that year and assistant doctor (Assistenzarzt) in 1912. Apart from working at the AKH, he also gave lectures on medicine in Viennese public education institutions. During the First World War he was a military doctor with the rank Oberarzt/Regimentsarzt and received numerous medals. After the war, he continued as an assistant doctor at the AKH and in 1921 completed his specialist training in internal medicine and opened a private practice in Vienna alongside his work at the hospital. He left the AKH on 27 March 1925 and was senior physician (Primararzt) and head (Vorstand) of the tuberculosis department of the municipal nursing home at Lainz Hospital until March 1938. Arnstein did not belong to the Gesellschaft der Ärzte in Wien. After the annexation to Nazi Germany, he and his family, who lived at Ferstelgasse 4 in the 9th district, were persecuted as Jews. Having been forced to retire on 23 April 1938, he fled with his wife and their two sons Hans and Heinrich Arnstein in August 1938 to Britain and worked from 1941 as a doctor in London. In his asset declaration of July 1938, he listed a private medical library. The Arnstein family's assets were seized by the Gestapo and became the property of the Reich in accordance with the Elfte Verordnung zum Reichsbürgergesetz (Eleventh Regulation on the Reich Citizenship Law) of 25 November 1941. Prior to that, the household had been auctioned by the Dorotheum in Vienna. After 1945, Arnstein submitted two claims to the Restitution Commission at the Landesgericht für Zivilrechtssachen (provincial court for civil law matters) in Vienna regarding the Reichsfluchtsteuer (Reich Flight Tax) he had been forced to pay and his title to property at Cobenzlgasse 55 in the 19th district. The Reich Flight Tax was not refunded and the second claim ended with a settlement. Arnstein died in London in 1972.

The systematic provenance research at then Zweigbibliothek für Geschichte der Medizin an der Universitätsbibliothek der Medizinischen Universität Wien revealed a book belonging to Alfred Arnstein that had been incorporated after March 1938 in the Bibliothek der Gesellschaft der Ärzte in Wien – Billrothaus. It was restituted in 2012 to Arnstein's legal successors.