Biržiška belonged to an eminent noble family. His grandfather Leonardas Biržiška was an active participant in the 1839-1831 Uprising; and his brothers, Vaclovas Biržiška and Viktoras Biržiška, were also leaders of the Lithuanian community. His father, the physician Antanas Biržiška, declined a professorship at the University of Moscow to practice medicine in the rural areas of Lithuania.