Swept shock wave/boundary layer interaction (SSBLI) is a typical flow phenomenon in hypersonic vehicles. Under the influence of lightweight structural design, the stiffness of the panel will be significantly reduced, which can easily lead to fluid–structure interaction (FSI) issues. Based on an in-house FSI program, the dynamical characteristics of the flexible panel and the influence of the FSI on flow characteristics was investigated by varying the area of a plate immersed in the separation zone induced by SSBLI. The results show that as the immersion area increases, the dominant mode of the panel changes from low-order to high-order, and the pressure and displacement response transition from limit cycle oscillation to multi-frequency irregular oscillation. The evolution of pressure pulsations at the line of surface-flow coalescence and the line of surface-flow divergence in the flow field is consistent with that of the panel. Furthermore, the degree of destruction of the quasi-conical characteristics increases with the increase in the immersed area. Moreover, as the displacement of the panel increases, the “depression” of the separation shock wave becomes more pronounced, and the expansion wave gradually strengthens and moves farther away from the sharp fin. This study provides an important reference for the refined design of aircraft under complex hypersonic flows.