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We report development and application of a fluid-structure interaction (FSI) solver for compressible flows with large-scale flow-induced deformation of the structure. The FSI solver utilizes partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structure dynamics solver. The flow solver is based on a higher-order finite-difference method on Cartesian grid and employs ghost-cell methodology to impose boundary conditions on the immersed boundary. A higher-order accuracy near the immersed boundary is achieved by combining the ghost-cell approach with a weighted least-square error method based on a higher-order approximate polynomial. The second order spatial accuracy of the flow solver is established by performing a grid refinement study. The structure solver is validated with a canonical elastostatics problem. The FSI solver is validated with published measurements and simulations for the large-scale deformation of a thin elastic steel panel subjected to blast loading in a shock tube. The solver correctly predicts oscillating behavior of the tip of the panel with reasonable fidelity and computed shock wave propagation is qualitatively consistent with the published results. In order to demonstrate the fidelity of the solver and to investigate coupled physics of the shock-structure interaction for a thin elastic plate, we employ the solver for simulating 6.4 kg TNT blast loading on the thin elastic plate. The initial conditions of the blast are taken from field tests reported in the literature. Using numerical schlieren, the shock front propagation, Mach reflection and vortex shedding at the tip of the plate are visualized during the shock wave impact on the plate. We discuss coupling between the non-linear dynamics of the plate and blast loading.