The distinct physical properties of hybrid organic-inorganic materials can lead to unexpected nonequilibrium phenomena that are difficult to characterize due to the broad range of length and time scales involved. For instance, mixed halide hybrid perovskites are promising materials for optoelectronics, yet bulk measurements suggest the halides reversibly phase separate upon photoexcitation. By combining nanoscale imaging and multiscale modeling, we find that the nature of halide demixing in these materials is distinct from macroscopic phase separation. We propose that the localized strain induced by a single photoexcited charge interacting with the soft, ionic lattice is sufficient to promote halide phase separation and nucleate a light-stabilized, low-bandgap, ∼8 nm iodide-rich cluster. The limited extent of this polaron is essential to promote demixing because by contrast bulk strain would simply be relaxed. Photoinduced phase separation is therefore a consequence of the unique electromechanical properties of this hybrid class of materials. Exploiting photoinduced phase separation and other nonequilibrium phenomena in hybrid materials more generally could expand applications in sensing, switching, memory, and energy storage.