Neutrino-electron scatterings (nu - e) are purely leptonic processes with robust standard model predictions. Their measurements can therefore provide constraints to physics beyond the standard model. Noncommutative (NC) field theories modify space-time commutation relations, and allow neutrino electromagnetic couplings at the tree level. Their contribution to the neutrino-electron scattering cross section was derived. Constraints were placed on the NC scale parameter Lambda(NC) from nu - e experiments with reactor and accelerator neutrinos. The most stringent limit of Lambda(NC) > 3.3 TeV at 95% confidence level improves over the direct bounds from collider experiments.