Particulate methane monooxygenase (pMMO) is an enzyme that oxidizes methane to methanol with high activity and selectivity. Limited success has been achieved in incorporating biologically relevant ligands for the formation of such active site in a synthetic system. Here, we report the design and synthesis of metal–organic framework (MOF) catalysts inspired by pMMO for selective methane oxidation to methanol. By judicious selection of a framework with appropriate topology and chemical functionality, MOF-808 was used to postsynthetically install ligands bearing imidazole units for subsequent metalation with Cu(I) in the presence of dioxygen. The catalysts show high selectivity for methane oxidation to methanol under isothermal conditions at 150 °C. Combined spectroscopies and density functional theory calculations suggest bis(μ-oxo) dicopper species as probable active site of the catalysts.