Silicon carbide (SiC) is utilized in the automotive, semiconductor, and aerospace industries because of its desirable characteristics. Nevertheless, the traditional machining method induces surface microcracks, low geometrical precision, and severe tool wear due to the intrinsic high brittleness and hardness of SiC. Femtosecond laser processing as a high-precision machining method offers a new approach to SiC processing. However, during the process of femtosecond laser ablation, temperature redistribution and changes in geometrical morphology features are caused by alterations in carrier density. Therefore, the current study presented a multi-physics model that took carrier density alterations into account to more accurately predict the geometrical morphology for femtosecond laser ablating SiC. The transient nonlinear evolutions of the optical and physical characteristics of SiC irradiated by femtosecond laser were analyzed and the influence of laser parameters on the ablation morphology was studied. The femtosecond laser ablation experiments were performed, and the ablated surfaces were subsequently analyzed. The experimental results demonstrate that the proposed model can effectively predict the geometrical morphology. The predicted error of the ablation diameter is within the range from 0.15% to 7.44%. The predicted error of the ablation depth is within the range from 1.72% to 6.94%. This work can offer a new way to control the desired geometrical morphology of SiC in the automotive, semiconductor, and aerospace industries.