Oxidation of methane with a hydrogen-air mixture at 70 °C and a partial pressure of methane of 30 atm was studied. Water-soluble glutathione-stabilized nanoclusters Aun (n = 18–25) were used as catalysts for this process. Methanol, methyl hydroperoxide (MeOOH), formaldehyde, and a small amount of CO2 were identified as the reaction products. Formation of H2O2 was also revealed; its maximum concentration was 0.5 mmol L−1, and it decreased fivefold in the presence of methane. The study of the reaction kinetics showed that the ratio of initial rates of formation of MeOH, MeOOH, and CH2O was 1: 1: 2. The reaction terminated after 9 h, MeOOH almost completely disappeared, whereas the concentrations of methanol and formaldehyde reached the stationary values of 0.6 and 0.4 mmol L−1, respectively. This phenomenon was observed despite the presence of both the oxidizing agent and the substrate in the reaction zone. Possibly, blockage of active sites by the reaction products took place at a certain time because once the volatile products were removed from the system and the gas phase was renewed, the catalyst showed a stable activity over several cycles. When H2 was excluded from the reaction system, the MeOH yield decreased sixfold, whereas the MeOOH yield tripled after 6 h of reaction. When NADH was used as a hydrogen source, the selectivity with respect to methanol decreased. With the use of quantum chemical calculations, a mechanism for the methane oxidation has been developed. It assumes the existence of the same intermediate as a precursor of all main reaction products.