Selective oxidation of methane to methanol is one of the most difficult chemical processes to perform. A potential group of catalysts to achieve CH4 partial oxidation are Cu-exchanged zeolites mimicking the active structure of the enzyme methane monooxygenase. However, the details of this conversion, including the structure of the active site, are still under debate. In this contribution, periodic density functional theory (DFT) methods were employed to explore the molecular features of the selective oxidation of methane to methanol catalyzed by Cu-exchanged mordenite (Cu-MOR). We focused on two types of previously suggested active species, CuOCu and CuOOCu. Our calculations indicate that the formation of CuOCu is more feasible than that of CuOOCu. In addition, a much lower C–H dissociation barrier is located on the former active site, indicating that C–H bond activation is easily achieved with CuOCu. We calculated the energy barriers of all elementary steps for the entire process, including catalyst activation, CH4 activation, and CH3OH desorption. Our calculations are in agreement with experimental observations and present the first theoretical study examining the entire process of selective oxidation of methane to methanol.