The instability mechanism based on the Coriolis force, especially on a rapidly rotating portable device handling shear-thinning fluids such as blood, is of utmost importance for eventual detection of diseases by mixing with suitable reagents. Motivated by this proposition, this study renders a modal stability analysis of shear-thinning fluids in a rotating microchannel modeled by the Carreau rheological law. When a microchannel is engraved with a rotating compact disk-based device, the centrifugal force acts as the driving force that actuates the flow and the Coriolis force enhances the mixing process in a significantly short span by destabilizing the flow. An Orr-Sommerfeld-Squire analysis is performed to explore the role of these forces on the linear stability of a rotating shear-thinning flow. Reported results on shear-thinning flow with streamwise disturbances indicate that the critical Reynolds number for the flow transition with viscosity perturbation is nearly half of that of the critical value for the same without viscosity perturbation. In sharp contrast, the present analysis considering spanwise disturbances reveals that the critical Reynolds numbers with and without viscosity perturbation remain virtually unaltered under rotational effects. However, the viscosity variation has no significant influence on the Coriolis force-based instability. Numerical results confirm that a momentous destabilization is possible with the use of the Coriolis force via generating secondary flow inside the channel. Interestingly, the roll cells corresponding to the instabilities at lower time constants exhibit the existence of two distinct vortices, and the center of the stronger one is essentially settled toward the unstable "stratified" region. Moreover, for a higher value of the time constant, only one vortex occupies the entire channel. This, in turn, may turn out to be of fundamental importance in realizing new instability regimes facilitating efficient mixing in rotationally actuated fluidic devices deployed for biochemical analysis and medical diagnostics. © 2020 Author(s).