The anaerobic oxidation of methane (AOM) is performed by methanotrophic archaea (ANME) in distinct sulfate-methane interfaces of marine sediments. In these interfaces, AOM often appears to deplete methane in the heavy isotopes toward isotopic compositions similar to methanogenesis. Here, we shed light on this effect and its physiological underpinnings using a thermophilic ANME-1-dominated culture. At high sulfate concentrations, residual methane is enriched in both 13C and 2H (13α = 1.016 and 2α = 1.155), as observed previously. In contrast, at low sulfate concentrations, the residual methane is substantially depleted in 13C (13α = 0.977) and, to a lesser extent, in 2H. Using a biochemical-isotopic model, we explain the sulfate dependence of the net isotopic fractionation through the thermodynamic drive of the involved intracellular reactions. Our findings relate these isotopic patterns to the physiology and environment of the ANME, thereby explaining a commonly observed isotopic enigma.