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Photosensitive azobenzene-containing surfactants have attracted great attention in past years because they offer a means to control soft-matter transformations with light. At concentrations higher than the critical micelle concentration (CMC), the surfactant molecules aggregate and form micelles, which leads to a slowdown of the photoinduced trans -> cis azobenzene isomerization. Here, we combine nonadiabatic dynamics simulations for the surfactant molecules embedded in the micelles with absorption spectroscopy measurements of micellar solutions to uncover the reasons responsible for the reaction slowdown. Our simulations reveal a decrease of isomerization quantum yields for molecules inside the micelles. We also observe a reduction of extinction coefficients upon micellization. These findings explain the deceleration of the trans -> cis switching in micelles of the azobenzene-containing surfactants.