The lunar exosphere is produced by a combination of processes including thermal desorption, micrometeoroid bombardment, internal gas release, photon-stimulated desorption, and charged-particle sputtering. Here we investigate an additional mechanism not previously considered for the Moon, namely the role that newly-born ions from the exosphere itself play in sputtering additional neutrals from the lunar surface, known as self-sputtering. Our calculations suggest that this process may sputter neutrals into the lunar exosphere at a rate equal to or greater than either charged-particle sputtering due to passage through the Earth's plasma sheet. We use known or modeled densities and distributions of exospheric neutrals, laboratory derived values for the photo-ionization rates and neutral sputtering yields, and knowledge of the ambient electromagnetic environment at the Moon to derive estimates of the self-sputtering yield. We present the spatial and temporal variation of the self-sputtering neutral flux and discuss the implications thereof.