In this work we investigate properties of ultra-narrow photoluminescence lines originating from recombination of excitons trapped by short-range potential fluctuations, caused by alloy disorder in GaAs/GaNAs core/shell nanowires. From power-dependent photoluminescence measurements we show that the emission behavior is consistent with biexciton-exciton cascade recombination in quantum dots. We also show that the thermal activation energy from the related localized states is of the order of 9–30 meV, suggesting a rather shallow confinement potential.