Long‐period magnetotelluric (MT) data can be used to interpret upper mantle temperature, hydrogen content, and the presence of partial melt, all of which strongly influence mantle viscosity. We have collected the first long‐period MT data in Svalbard and have combined them with pre‐existing broadband MT data to produce a model of the electrical resistivity of Svalbard's upper mantle. Asthenospheric resistivities are low compared to stable continental settings but more comparable to young oceanic asthenosphere, suggesting that the physical state of Svalbard's upper mantle is controlled by its proximity to the Mid‐Atlantic Ridge. Interpretation of the MT model using a petrologically‐constrained genetic algorithm approach shows that partial melt is present in the uppermost asthenosphere beneath Svalbard. This is the first direct evidence of partial melt in Svalbard's asthenosphere from deep geophysical soundings. Viscosities calculated from the geophysical data show a low viscosity layer (~1018 Pa s) coincident with the partial melt layer, underlain by a higher viscosity layer (~1020 Pa s) extending to the transition zone. Viscosities calculated from glacial isostatic adjustment (GIA) data in Svalbard show a considerable range due mainly to uncertainties in past ice sheet models. Improved constraints on Svalbard's mantle viscosity from geophysical data may help to improve these GIA models.