The boundary effect on the movement of a particle in a Carreau fluid is investigated theoretically by considering the sedimentation of a cylindrical particle along the axis of a cylindrical tube. The influences of the key parameters of the system under consideration on the drag coefficient and the associated flow field are discussed. These include the relaxation time constant and the power-law index of a Carreau fluid, the length of a particle, and the diameter of a cylindrical tube. We show that the flow field and the drag coefficient are affected more significantly by the boundary effect, measured by the ratio (particle diameter/tube diameter) than by the size of a particle and the properties of the fluid. In general, the terminal velocity of a particle correlates nonlinearly with the ratio (particle diameter/tube diameter). The problem of a particle in an unbounded fluid can be recovered as a limiting case of the present one.