The dynamic effects of the lateral karst cavity on the shield tunnels under different incident angles of seismic waves are investigated by numerical analysis in this paper, based on the Dalian Metro Line 5 project. The viscous-spring artificial boundary is applied and verified to guarantee the accuracy of seismic input. A simplified finite element model of shield tunnel is established based on the equivalent bending stiffness model. This paper compares the seismic response characteristics and damage states of the tunnel under different incident angles by analyzing the axial deformation, stress distribution, and damage severity, respectively. A new damage state classification criterion is proposed by introducing the relationship between cracks and tensile damage. The results show that the tunnel’s affected scope by the lateral karst cavity is twice the cavity diameter. As the incident angle increases, the tunnel’s displacement and stress increase and show the structural spatial difference, and the tunnel’s damage state is increasingly severe. The displacement and stress reach the max values when the incident angle is 30°. The cracks along the axial direction extend on the outer surface of the vault and bottom, and the crack width is greater than 0.2 mm, as that angle is 30°. The damage severity at the tunnel’s central zone is minimum along axial directions during seismic action, while the damage concentration occurs on the bottom at the end of seismic. The lateral karst cavity plays an energy dissipation and vibration reduction role to a certain extent, but it also aggravates the local damage. This paper can serve as a reference for the seismic design of tunnels in karst regions.