Methane is a promising gaseous biosignature on rocky exoplanets, given a suitable context. Establishing the robustness of methane biosignatures on rocky exoplanets requires assessing potential “false positive” production pathways that could yield large fluxes of methane of abiotic origin. Here we modeled the flux of abiotic methane production from graphite hydrogenation on the surface of Mercury, where a relatively carbon-rich crust and bombardment by solar protons might favor this reaction. We calculated negligible methane flux from this abiotic reaction compared to biological methane flux on Earth. Graphite hydrogenation would only be expected to yield significant methane fluxes on exoplanets with high temperatures and ion fluxes that would preclude habitability for life as we know it. Thus, graphite hydrogenation by stellar wind can likely be ruled out as a potential “false positive” methane biosignature source.