The single relaxation D2Q9 lattice Boltzmann method (LBM) is run in the current research beside the generalized power law model for simulation of non‐Newtonian magneto‐hydrodynamics (MHD) laminar flow field inside a channel with local symmetric constriction. Analytical results of non‐Newtonian fluid flow in a channel without magnetic field, as well as Newtonian fluid flow at various Hartmann No., are used to validate the numerical model. Then, fluid flow simulation is performed for non‐Newtonian fluid with different power law index at various Hartmann No. (Ha) whereas Reynolds No. are set to be constant in all cases. The present non‐Newtonian fluid can be achieved by adding various nanoparticles such as MWCNT to the base fluid. To explore the effect of magnetic Reynolds No. (Re_m), the fluid flows with different magnetic resistivity are also simulated. Results show that the separation can be controlled by a magnetic field with the penalty of larger friction coefficient and pressure loss along the channel length. In fact, for a specified Re_m, the higher the Ha, the larger the pressure loss. It is also observed that the pressure loss is larger for fluids flow with higher power law index and lower Re_m.