Understanding the mechanisms of light–matter interactions in ultra-small plasmonic nanoparticles (USNP) represents a major challenge because of the importance of size dependence and quantum effects. The plasmon resonance in such small metallic nanoparticles (< 5 nm) exhibits substantial deviation from classical theory predictions, with evident frequency shifts to a higher energy. This is due to the quantum nature of the free charge carriers and the dynamic response of metallic nanoparticle to the self-consistent electromagnetic fields. Such phenomena have so far been poorly understood in experiments while classical theory has mostly focused on nanostructures and sidestepped the size dependence. Here we report a quantum mechanical model of the metal permittivity to describe the USNP behaviour and experimental evidence. The proposed non-local quantum model of the permittivity for the propagation of plasmon waves in quantum-confined silver nanoparticles has no size limitations in the UNSP range.