  We consider the impact of neutral-current (NC) non-standard neutrino
interactions (NSI) on the determination of the neutrino mass ordering. We show
that in presence of NSI there is an exact degeneracy which makes it impossible
to determine the neutrino mass ordering and the octant of the solar mixing
angle $\theta_{12}$ at oscillation experiments. The degeneracy holds at the
probability level and for arbitrary matter density profiles, and hence, solar,
atmospheric, reactor, and accelerator neutrino experiments are affected
simultaneously. The degeneracy requires order-one corrections from NSI to the
NC neutrino--quark interaction and can be tested in neutrino--nucleus NC
scattering experiments.
