Abstract: Many scenarios of new physics predict the existence of neutrino nonstandard interactions, new vector contact interactions between neutrinos, and first generation fermions beyond the Standard Model. We obtain model-independent constraints on the Standard Model effective field theory at high energies from bounds on neutrino nonstandard interactions derived at low energies. Our analysis explores a large set of new physics scenarios and includes full one-loop running effects below and above the electroweak scale. Our results show that neutrino nonstandard interactions already push the scale of new physics beyond the TeV. We also conclude that bounds derived by other experimental probes, in particular by low-energy precision measurements and by charged lepton flavor violation searches, are generally more stringent. Our study constitutes a first step toward the systematization of phenomenological analyses to evaluate the impact of neutrino nonstandard interactions for new physics scenarios at high energies.