 Kellner was born in Vaihingen an der Enz, a town on the Enz River in southern Germany.At the time of his birth, Vaihingen was part of the Kingdom of Württemberg in the German Empire.Kellner was the only child of Georg Friedrich Kellner, a baker and confectioner from the town of Arnstadt in Thuringia, and Barbara Wilhelmine Vaigle from Bietigheim-Bissingen near Ludwigsburg.