Schwab received honours throughout his lifetime in recognition of his scientific work. In 1952 he became one of the only 45 ordinary members of the Bavarian Academy of Sciences, and in 1956 he was also inducted as a member of the Heidelberg Academy of Sciences and the German National Academy of Sciences Leopoldina.
In 1960 he was awarded the Liebig Medal of the German Chemical Society; he had also been awarded the Order of the Crown of Belgium (Officer class) as well as the Golden Cross of the Greek Order of George I.
Additionally, he was conferred honorary doctorates from the Sorbonne, the Free University of Berlin and the University of Liège, as well as an honorary professorship at the Central University of Venezuela.