Our understanding of the dielectric response of interfacial water, which underlies the solvation properties and reaction rates at aqueous interfaces, relies on the linear response approximation: an external electric field induces a linearly proportional polarization. This implies antisymmetry with respect to the sign of the field. Atomistic simulations have suggested, however, that the polarization of interfacial water may deviate considerably from the linear response. Here we present an experimental study addressing this issue. We measured vibrational sum-frequency generation spectra of heavy water (D2O) near a monolayer graphene electrode, to study its response to an external electric field under controlled electrochemical conditions. The spectra of the OD stretch show a pronounced asymmetry for positive versus negative electrode charge. At negative charge below 5 × 1012 electrons per square centimetre, a peak of the non-hydrogen-bonded OD groups pointing towards the graphene surface is observed at a frequency of 2,700 per centimetre. At neutral or positive electrode potentials, this 'free-OD' peak disappears abruptly, and the spectra display broad peaks of hydrogen-bonded OD species (at 2,300-2,650 per centimetre). Miller's rule1 connects the vibrational sum-frequency generation response to the dielectric constant. The observed deviation from the linear response for electric fields of about ±3 × 108 volts per metre calls into question the validity of treating interfacial water as a simple dielectric medium.