Transition-metal-catalysed carbenoid insertion of hydroxyl groups represents a robust and versatile method to forge C–O bonds. Achieving site-selective functionalization of alcohols using this transformation has undoubted synthetic value but remains challenging. Here we report a strategy for selective carbenoid O–H insertion that exploits an engineered heterogeneous iridium single-atom catalyst, thus providing opportunities for organic transformations by merging material science and catalysis. This catalytic protocol delivers excellent selectivities (up to 99:1) for the functionalization of aliphatic over phenolic O–H bonds, whereas the analogous homogeneous catalyst, Ir(ttp)COCl (ttp = 5,10,15,20-tetra-p-tolylporphyrinato), provided modest preferences. Density-functional-theory calculations suggest that the site-selectivity derives from the lower oxidation state of the iridium metal centre in the heterogeneous catalyst and its impact on the absorption energies of the reactants. These results showcase an example of a heterogeneous single-atom catalyst providing superior site-selectivity and provide a complementary strategy to address challenges in catalysis for organic synthesis. [Figure not available: see fulltext.]