In this paper, the interaction between cylindrical particles and shear-thinning non-Newtonian fluids in a linear shear flow is investigated using particle-resolved direct numerical simulation. The Carreau model is used to represent the rheological properties of shear-thinning fluids, and the numerical method is validated against previously published data. Then, the effects of Reynolds number (Re), aspect ratio (Ar), power-law index (n), Carreau number (Cu), and incident angle (α) on drag coefficient (CD), lift coefficient (CL), and torque coefficient (CT) of cylindrical particles are investigated. The numerical results show that the flow field structure and pressure distribution around the cylindrical particle in a shear flow are different from those in a uniform flow, and the particles in a shear flow generate extra CL and CT. Furthermore, comparing with Newtonian fluids, the shear-thinning properties of the non-Newtonian fluid change the viscosity distribution and significantly decrease the CD, CL, and CT of the particles. The variation laws and influencing mechanisms of CD, CL, and CT under different working conditions are discussed by dividing the total coefficients into pressure and viscous shear contributions. Predictive correlations of CD, CL, and CT are established by considering the effects of Re, Ar, n, Cu, and α. The findings indicate that both the shear flow mode and shear-thinning properties must be considered when evaluating relevant particle–fluid interactions, which provides important guidance for predicting and controlling the orientation and distribution of cylindrical particles in shear-thinning fluids. Meanwhile, the predictive correlations can be used for large-scale simulations of multiphase coupling.