The drag on a spherical particle is studied for two limiting cases, namely for the rigid sphere and for the bubble. An approximate solution is found for creeping flow around a particle suspended in a shear-thinning fluid. The three parameter Carreau model is used to represent the suspending liquid. The drag force on the particle for both cases is calculated by a perturbation method around the Newtonian solution in the limit of small Carreau number. The resulting expressions are found to be dependent on the Carreau number and on the power-law index.