The transport of heat and mass from the surface of a cylinder coated with a catalyst and subject to an impinging flow of a Casson rheological fluid is investigated. The cylinder features circumferentially non-uniform transpiration and is embedded inside a homogenous porous medium. The non-equilibrium thermodynamics of the problem, including Soret and Dufour effects and local thermal non-equilibrium in the porous medium, are considered. Through the introduction of similarity variables, the governing equations are reduced to a set of non-linear ordinary differential equations which are subsequently solved numerically. This results in the prediction of hydrodynamic, temperature, concentration and entropy generation fields, as well as local and average Nusselt, Sherwood and Bejan numbers. It is shown that, for low values of the Casson parameter and thus strong non-Newtonian behaviour, the porous system has a significant tendency towards maintaining local thermal equilibrium. Furthermore, the results show a major reduction in the average Nusselt number during the transition from Newtonian to non-Newtonian fluid, while the reduction in the Sherwood number is less pronounced. It is also demonstrated that flow, thermal and mass transfer irreversibilities are significantly affected by the fluid’s strengthened non-Newtonian characteristics. The physical reasons for these behaviours are discussed by exploring the influence of the Casson parameter and other pertinent factors upon the thickness of thermal and concentration boundary layers. It is noted that this study is the first systematic investigation of the stagnation-point flow of Casson fluid in cylindrical porous media.