The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.