In this work, the combined effects of contamination and shear-thinning (power-law) viscosity on the free rise of a single bubble have been studied numerically. The influence of insoluble contaminants on the surface of the bubble has been incorporated in the analysis by employing the spherical stagnant cap model which has been employed successfully in Newtonian fluids. The governing differential equations have been solved numerically over a range of conditions: Reynolds number, Re = 10-200; power-law index, n = 0.6-1; and stagnant cap angle, alpha = 0 degrees-180 degrees. Finally, the effect of each of the parameters-namely, Re, n, and alpha-on streamline patterns, surface pressure and vorticity distributions, and individual and total drag coefficients is discussed in detail. Briefly, for alpha > 30 degrees and Re >= 50, the recirculation length increases and the separation angle moves forward with the increasing Re; however, mixed trends are observed with respect to the power law index and the stagnant cap angle. The total drag coefficient increases as the cap angle and/or the power-law index increases and/or the Reynolds number decreases; while mixed trends are observed on the dependence of the ratio of the individual drag coefficients on these parameters.