In this study, the hydromagnetic Blasius flow of power‐law nanofluids is investigated numerically. A convectively heated impermeable vertical plate is used and a constant transverse magnetic field is applied at the plate surface. The characteristics of water‐based non‐Newtonian nanofluids are explored using a non‐Newtonian power‐law model. A Buongiorno model is employed to include the effects of Brownian motion and thermophoresis in the study. The governing mass, momentum, thermal energy, and nanoparticle concentration equations are transformed into nonlinear ordinary differential equations which are solved using a spectral relaxation method. The effects of nanofluid parameters (), power index , generalized Prandtl (), and Schmidt () numbers on dimensionless velocity, temperature, concentration, skin friction, local Nusselt, and Sherwood numbers are explored. It is found that pseudoplastic nanofluids have higher skin friction and lower heat and mass transfer rates than dilatant nanofluids.