Tunnels built in geologically active areas are prone to severe damage due to fault dislocation and subsequent earthquakes. Using the Ngong tunnel in the East African Rift Valley as an example, the dynamic response of a fault-crossing tunnel and the corresponding sensitivity are numerically simulated by considering four factors, i.e., tunnel joint stiffness, isolation layer elastic modulus, strike-slip fault creep-slip and earthquakes. The results show that a valley-shaped propagation of peak displacement at the tunnel invert occurs in the longitudinal axis direction under an earthquake alone. Then, it transforms into an S-shaped under strike-slip fault creep-slip and subsequent seismic shaking. The tunnel invert in the fault zone is susceptible to tensile and shear failures under strike-slip fault creep-slip movements of less than 15 cm and subsequent seismic shaking. Furthermore, the peak tensile and shear stress responses of the tunnel invert in the fault zone are more sensitive to fault creep-slip than earthquakes. They are also more sensitive to the isolation layer elastic modulus compared to the joint stiffness of a segmental tunnel with two segments. The stress responses can be effectively reduced when the isolation layer elastic modulus logarithmic ratio equals −4. Therefore, the isolation layer is more suitable to mitigate the potential failure under small strike-slip fault creep-slip and subsequent seismic shaking than segmental tunnels with two segments. The results of this study can provide some reference for the disaster mitigation of fault-crossing tunnels in terms of dynamic damage in active fault zones.