Knowledge of the pore-scale physics of underground multiphase flows is essential to devise efficient soil remediation methods. However, the immiscible displacement of pollutant through the injection of a shear-thinning fluid remains poorly understood. The current work presents a full set of direct numerical simulations in which a Newtonian contaminant is displaced by a Carreau fluid or, alternatively, by a Newtonian fluid, in three porous media with different degrees of microstructural complexity. Imbibition, drainage and neutral wettability cases are considered, and the sensitivity of residual pollutant saturation to Carreau's law parameters is also assessed. The present results allow for the quantification of the performance of immiscible displacement using shear-thinning invading fluids. This performance is shown to depend on the value of capillary number and the heterogeneity of the porous microstructure, which determine the relative importance of viscous fingering, capillary forces and pollutant trapping behind the invasion front.