The motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow is studied using a boundary element numerical simulation. Non-linear effects from the dependency of the viscosity on the velocity field are treated in an implicit manner and the resultant domain integral is transformed into an equivalent series of boundary integrals using the Dual Reciprocity Method. The non-homogeneous (non-linear) system of algebraic equations resulting from the discretization of the boundary element formulation is solved using a modified Newton-Raphson method for drops with values of the power law index of n = 0.8 and 0.6 and compared to the corresponding Newtonian cases (n = 1). The viscosity of the fluid inside the drop follows the truncated power law model. By using this model, the shear-thinning behaviour of the viscosity is correctly represented while avoiding the shear thickening which can be observed using the standard power law in small gradient flows. The simulations showed that the non-Newtonian drops had larger deformations than the corresponding Newtonian drops due to a general decrease in the viscosity. The value of the local viscosities was found to be dependant not only on the velocity field created by the motion of the internal cylinder, but strongly dependant on the surface tension forces. The rate of deformation of the drops was greater in the beginning of the simulation and decreased toward the end showing the drops found a more or less stable shape.