This English translation of the paper by F. Zwicky, "Die Rotverschiebung von extragalaktischen Nebeln", Helv. Phys. Acta 6, 110-127 (1933), in which he concluded from the results of observations that the amount of non-luminous matter in the Universe must be greater than that of luminous matter-thus becoming an early precursor of the dark matter idea, has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. The paper is accompanied by an editorial note written by Jurgen Ehlers and by Zwicky's brief biography compiled by Andrzej Krasi angstrom"ski.