Numerical investigations are performed on the magnetohydrodynamic (MHD) pump-based microchannel cooling system for heat dissipating element. In the present study, the MHD pump performance is evaluated considering normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity by varying applied voltage and Hartmann number. It is found that for a low Hartmann number, the Lorentz force increases with an increase in applied voltage and Hartmann number. The velocity distribution along dimensionless width, the shear stress distribution along dimensionless width, the magnetic flux density along the dimensionless width and radial magnetic field distribution showed symmetrical behavior. The MHD pump-based microchannel cooling system performance is evaluated by considering the maximum temperature of the heat dissipating element, heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, the influence of various nanofluids including Cu-water, TiO2-water and Al2O3-water nanofluids on heat transfer performance of MHD pump-based microchannel is evaluated. As the applied voltage increased from 0.05 V to 0.35 V at Hartmann number 1.41, the heat removal rate increased by 39.5%. The results reveal that for low Hartmann number, average Nusselt number is increasing function of applied voltage and Hartmann number. At the Hartmann number value of 3.74 and applied voltage value of 0.35 V, average Nusselt numbers were 12.3% and 15.1% higher for Cu-water nanofluid compared to TiO2-water and Al2O3-water nanofluids, respectively. The proposed magnetohydrodynamic microcooling system is effective without any moving part.