A model is proposed for characterizing exosome size distributions based on dynamic scaling of domain growth on the limiting membrane of multivesicular bodies in the established exosome biogenesis pathway. The scaling exponent in this model captures the asymmetry of exosome size distributions, which are notably right-skewed to larger vesicles, independent of the minimum detectable vesicle size. Analyses of exosome size distributions obtained by cryogenic transmission electron microscopy imaging and nanoparticle tracking show, respectively, that the scaling exponent is sensitive to the state of the cell source for exosomes in cell culture supernatants and can distinguish exosome size distributions in serum samples taken from cancer patients relative to those from healthy donors. Finally, we comment on mechanistic differences between our dynamic scaling model and random fragmentation models used to describe size distributions of synthetic vesicles.