One of the major open questions in particle physics is the issue of the neutrino mass ordering (NMO). The current data of the two long-baseline experiments NOνA and T2K, interpreted in the standard three-flavor scenario, provide a ∼2.4σ indication in favor of the normal neutrino mass ordering. We show that such an indication is completely washed out if one assumes the existence of neutral-current nonstandard interactions (NSI) of the flavor changing type involving the e-τ flavors. This implies that the claim for a discovery of the NMO will require a careful consideration of the impact of hypothetical NSI.