Julius Drey was born in Vienna on 1 May 1858, the son of Lazarus Drey and Babette, née Cohn. He studied in the Medical Faculty of the University of Vienna and completed his doctorate in 1882. Thereafter he worked in the General Hospital (AKH) as an assistant physician and surgeon in the 1st Obstetric Clinic. In 1886 he became head of the Erstes öffentliches Kinderkrankeninstitut (First Public Paediatric Hospital). From 1899 to 1938 he also had a practice at his home, Wipplingerstraße 13 in Vienna's 1st district. He was a member of the paediatric section of the Gesellschaft für innere Medizin und Kinderheilkunde (Internal Medicine and Paediatrics Society) in Vienna and joined the Wiener Ärztekammer in 1894. In 1893 he married Louise (Aloisie), née Kraus, a sister of the Austrian writer Karl Kraus, born on 22 July 1863 in Jitschin, Bohemia (now Jičín, Czech Republic). The couple had no children. They were of Jewish origins and persecuted by the Nazis as Jews after the annexation of Austria to the German Reich. As Jewish doctors were forbidden from working, Julius Drey closed his practice on 17 July 1938. In a letter from Aloisie to the Vermögensverkehrsstelle (Property Transaction Office) of December 1938, she stated that the couple had had no income since July 1938 and at the end of the year were completely without means. Julius Drey died on 29 April 1939 at the age of eighty-one in his apartment in Vienna and was buried on 3 May in the Central Cemetery. Aloisie Drey was deported on 22 July 1942 to the Theresienstadt ghetto and murdered on 10 October 1942. Her last place of abode before deportation was the collective housing at Czerningasse 4/5 in the 2nd district.

During provenance research at the Zweigbibliothek für Geschichte der Medizin an der Universitätsbibliothek der Medizinischen Universität Wien a book belonging to Julius Drey with the stamp "Dr. Julius Drey Wien I. Stubenbastei 10" was discovered. According to the inventory and the handwritten entry in the book itself, the former Institutsbibliothek für Geschichte der Medizin (history of medicine departmental library) had acquired it on 25 May 1949 from Antiquariat Alfred Wolf, which had been active in Nazi book looting. The heirs are currently being sought so the book can be restituted.