A boundary-layer analysis is presented for the mixed convection in an axisymmetric flow of a non-Newtonian nanofluid on a vertical cylinder. The micropolar model is chosen for the non-Newtonian fluid since the spinning motion of the nanoparticles as they move along the streamwise direction can be best described by the micropolar fluid model. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the micropolar material parameters, Brownian motion parameter N_b, thermophoresis parameter N_t and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. Two flow regions, namely, the buoyancy-assisted and buoyancy-opposed cases, are considered.