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 (alpha) on drag coefficient (C-D), lift coefficient (C-L), and torque coefficient (C-T) 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 C-L and C-T. Furthermore, comparing with Newtonian fluids, the shear-thinning properties of the non-Newtonian fluid change the viscosity distribution and significantly decrease the C-D, C-L, and C-T of the particles. The variation laws and influencing mechanisms of C-D, C-L, and C-T under different working conditions are discussed by dividing the total coefficients into pressure and viscous shear contributions. Predictive correlations of C-D, C-L, and C-T are established by considering the effects of Re, Ar, n, Cu, and alpha. 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.