In recent years, nanofluids have attracted attention as a new generation of heat transfer fluids in building heating, heat exchangers, plants, and automotive cooling applications because of their excellent thermal performance. Various benefits of the application of nanofluids include improved heat transfer, heat transfer system size reduction, minimal clogging, microchannel cooling, and miniaturization of systems. In this paper, a study of steady, laminar, natural convection boundary-layer flow adjacent to a vertical cylinder embedded in a thermally stratified nanofluid-saturated non-Darcy porous medium is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and a generalized porous media model, which includes inertia and boundary effects, is employed. The cylinder surface is maintained at a constant nanoparticles volume fraction, and the wall temperature is assumed to vary with the vertical distance according to the power law form. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved by Keller box method. A comparison is made with the available results in the literature, and our results are in very good agreement with the known results. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity, temperature, and volume fraction, as well as local shear stress and local Nusselt and Sherwood numbers, are presented graphically. The salient features of the results are analyzed and discussed. The results indicate that, when the buoyancy ratio or modified Grashof number increases, all of the local shear stress, local Nusselt number, and the local Sherwood number enhance while the opposite behaviors are predicted when the thermophoresis parameter increases. Moreover, increasing the value of the surface curvature parameter leads to increases in all of the local shear stress and the local Nusselt and Sherwood numbers while the opposite behaviors are obtained when either of the thermal stratification parameter or the boundary effect parameter increases.