Intermixed light-matter quasi-particles—polaritons—have unique optical properties owing to their compositional nature. These intriguing hybrid states have been extensively studied over the past decades in a wide range of realizations aiming at both basic science and emerging applications. However, recently, it has been demonstrated that not only optical but also material-related properties, such as chemical reactivity and charge transport, may be significantly altered in the strong coupling regime of light-matter interactions. We show that a nanoscale system, composed of a plasmonic nanoprism strongly coupled to excitons in a J-aggregated form of organic chromophores, experiences modified excited-state dynamics and, therefore, modified photochemical reactivity. Our experimental results reveal that photobleaching, one of the most fundamental photochemical reactions, can be effectively controlled and suppressed by the degree of plasmon-exciton coupling and detuning. In particular, we observe a 100-fold stabilization of organic dyes for the red-detuned nanoparticles. Our findings contribute to understanding of photochemical properties in the strong coupling regime and may find important implications for the performance and improved stability of optical devices incorporating organic dyes.