Nature is a valuable source of inspiration in the design of catalysts, and various approaches are used to elucidate the mechanism of hydrogenases, the enzymes that oxidize or produce H2. In FeFe hydrogenases, H2 oxidation occurs at the H-cluster, and catalysis involves H2 binding on the vacant coordination site of an iron centre. Here, we show that the reversible oxidative inactivation of this enzyme results from the binding of H2 to coordination positions that are normally blocked by intrinsic CO ligands. This flexibility of the coordination sphere around the reactive iron centre confers on the enzyme the ability to avoid harmful reactions under oxidizing conditions, including exposure to O2. The versatile chemistry of the diiron cluster in the natural system might inspire the design of novel synthetic catalysts for H2 oxidation.