The understanding of flow processes involving non-Newtonian fluids in the subsurface is of interest for many engineering applications, from in-situ remediation to enhanced oil recovery. The fluids of interest in such applications (f.e., polymers in remediation) often present shear-thinning properties, i.e., their viscosity decreases as a function of the local shear rate. We investigate how fracture wall roughness impacts the flow of a shear-thinning fluid. Numerical simulations of flow in 3D fracture geometries are carried out by solving a modified Navier-Stokes equation incorporating the Carreau viscous-shear model. The synthetic fractures consist of two rough surfaces which are isotropic self-affine geometries and correlated with each other above a scale which we denote correlation length (see Méheust et al. PAGEOPH 2003). Perfect plastic closing is assumed when the surfaces touch each other. The objective is to test how varying the correlation length impacts the flow behavior, for different degrees of closure, and how this behavior diverges for shear-thinning fluids from what is known for Newtonian fluids. The results from the 3D simulations are also compared to 2D simulations based on the lubrication theory, which we have developed as an extension of the Reynolds equation for Newtonian fluids. We also discuss the implications of our results for the general understanding of the flows of shear-thinning fluids in fractured media and of solute transport by such flows. References: Méheust, Y., & Schmittbuhl, J. (2003). Scale effects related to flow in rough fractures. Pure and Applied Geophysics, 160(5-6), 1023-1050.