Grünbaum was born to Jewish parents at Seligenstadt, Hesse, and studied philology and philosophy at the Universities of Giessen and Bonn.
[3][4] In addition to his own well-tended book collection, he made use of the extensive holdings of the Bavarian State Library.
[5] Following the model of Moritz Steinschneider for Oxford, Leyden, Hamburg, Berlin, and Munich itself, Grünbaum undertook the re-cataloguing of the Library's Hebrew holdings.
[5] He was confined to his room from 1892 as a result of increasing physical and then mental deterioration, but kept himself lively with his scholarly ideas and plans.
[6] After 1862 nearly all his papers on Oriental philology and folklore had appeared in the Zeitschrift der Deutschen Morgenländischen Gesellschaft; and after his death they were re-edited by Felix Perles under the title Gesammelte Aufsätze zur Sprach- und Sagenkunde (Berlin, 1901).