We present a stringy mechanism to generate Dirac neutrino masses by D-instantons in an experimentally relevant mass scale without fine-tuning. Within type IIA string theory with intersecting D6-branes, we spell out specific conditions for the emergence of such couplings and provide a class of supersymmetric local SU(5) grand unified models, based on the Z2 × Z'2 orientifold compactification, where perturbatively absent Dirac neutrino masses can be generated by D2-brane instantons in the experimentally observed mass regime, while Majorana masses remain absent, thus providing an intriguing mechanism for the origin of small neutrino masses due to nonperturbative stringy effects.