When nanoparticles (NPs) collide with low velocities, they interact elastically in the sense that--besides their fusion caused by their mutual van-der-Waals attraction--no defects are generated. We investigate the minimum velocity, vc, necessary for generating defects and inducing plasticity in the NP. The determination of this elastic-plastic threshold is of prime importance for modeling the behavior of granular matter. Using the generic Lennard-Jones interaction potential, we find vc to increase strongly with decreasing radius. Current models do not agree with our simulations, but we provide a model based on dislocation emission in the contact zone that quantitatively describes the size dependence of the elastic-plastic transition.