We investigate the spatial dependence of the exciton lifetimes in single ZnO nanowires. We have found that the free exciton and bound exciton lifetimes exhibit a maximum at the center of nanowires, while they decrease by 30% towards the tips. This dependence is explained by considering the cavity-like properties of the nanowires in combination with the Purcell effect. We show that the lifetime of the bound-excitons scales with the localization energy to the power of 3/2, which validates the model of Rashba and Gurgenishvili at the nanoscale.