We have performed room-temperature time-resolved photoluminescence measurements on samples that comprise InGaN insertions embedded in GaN nanowires. The decay curves reveal non-exponential recombination dynamics that evolve into a power law at long times. We find that the characteristic power-law exponent increases with emission photon energy. The data are analyzed in terms of a model that involves an interplay between a radiative state and a metastable charge-separated state. The agreement between our results and the model points towards an emission dominated by carriers localized on In-rich nanoclusters that form spontaneously inside the InGaN insertions.