The pressure driven flow of power-law fluids in microchannels subject to electrokinetic effects is analyzed in this work. The Cauchy momentum equation together with the power-law fluid constitutive equation is used to describe the power-law fluid flow in a slit microchannel with consideration of a body force resulting from the interaction of the charge density in the electrical double layer of the channel and the flow-induced electrokinetic potential. By using an appropriate approximate scheme, an expression for the induced streaming potential is obtained. The velocity profile, volumetric flow rate, apparent viscosity and friction coefficient are analytically evaluated, and the influencing factors including ionic concentration, wall zeta potential, flow behavior index and pressure difference are investigated. It is found that the pseudoplastic fluids are more susceptible to electokinetic effects than the dilatant fluids and then the flow characteristics of the pseudoplastic fluids are found to deviate drastically from those of Newtonian fluids.