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In polymer flooding, the primary attentions focused on the influence of polymer concentration and the elasticity on fluid breakup. However, the shear-thinning characteristic can also significantly affect the apparent viscosity of the fluid. We simulated the breakup process of the dispersed phase in both shear-thinning and Newtonian fluids by using volume of fluid method, encompassing various viscosity ratios, capillary numbers, and rheological parameters. The critical conditions of capillary number and viscosity ratio for breakup of the dispersed phase were obtained, indicating that the dispersed phase was more prone to breakup in shear-thinning fluids. The mechanism of fluid breakup induced by shear-thinning was examined through the analysis of viscosity, pressure, and the magnitude of vorticity. Attributed to heightened destabilization in the radial direction and diminished viscous forces, fluid breakup processes were enhanced by lower zero-shear viscosity and reduced power-law index. The fluid breakup caused by the radial instability of shear-thinning fluids is distinguishing from the classical Roof snap-off theory. Inspiring by these results, enhancing rheological parameters such as power-law index and zero-shear viscosity in designing polymer flooding technique can accelerate the occurrence of the breakup process, thereby achieving control over the oil recovery process. [Display omitted] • Volume of fluid method is utilized to simulate fluid breakup in pore-throat. • The fluid breakup is more susceptible to occur in surrounding shear-thinning fluids. • Breakup processes are enhanced in lower zero-shear-viscosity and power-law index. • Delaying effect of rheological parameters on breakup follows: power-law index > zero-shear-viscosity > relaxation time. [ABSTRACT FROM AUTHOR]