The characteristics of vortical structures in T-shaped branches with respect to the shear-thinning effect are numerically investigated using a power-law fluid model. By varying the power-law index n, we observe three different flow structures, namely, steady-, harmonic-, and turbulent-like regimes. The time-averaged and instantaneous vortical structures are examined for different values of the local Reynolds number. In the steady regime, stationary vortical structures form near the corners of the T-shaped branch. As n decreases, the vortical structures oscillate back and forth, giving rise to the harmonic regime. Decreasing n further, we observe the turbulent-like regime. In this regime, the vortical structures are torn off near the tips of the vortices and small-scale structures are vigorously generated, constituting more violent behavior than in the harmonic regime. If the local Reynolds number near the wall and near the cores of the vortical structures reaches a critical value, the flow structure becomes turbulent-like after the bifurcation of the T-shaped branch. In addition, the modal characteristics of the vortical structures are analyzed using dynamic mode decomposition with respect to the degree of shear-thinning. As shear-thinning appears in the flow, various high-frequency modes with small-scale vortical structures are observed, and their energies are evenly distributed. This supports the present observation of the vortical structures depending on shear-thinning and -thickening.