In this paper, the flow of power-law fluid over a circular cylinder near a moving wall is simulated numerically using a finite volume method for different Reynolds numbers (Re = 1, 10, 40), gap ratios (G/D = 0.2-1.0), and power-law indices (n = 0.5-1.5). The effects of fluid inertia, wall proximity, and rheological property on the drag and lift coefficient, gap flow characteristics, and recirculation modes are studied. Possible mechanisms for the variation of the drag and lift coefficient and the change in recirculation mode are addressed. The results show that the decrease in G/D or Re results in the increase in drag and lift coefficient, while the effect of n is dependent on Re and G/D. For the drag coefficient, shear-thickening fluid is more sensitive to the change of G/D. The variation of the lift coefficient can be explained by the movement of angular position of the front stagnation point. The redistribution of the flow around the cylinder results in different recirculation modes. Five distinct modes are found and the critical value of G/D for the mode change decreases with the decrease in n and increase in Re. Variation of the relative vortex intensity and the relative flow intensity nearby leads to the change of recirculation mode.