We present an Embedded Boundary method for the interaction between an inviscid compressible flow and a fragmenting structure. The fluid is discretized using a Finite Volume method combining Lax-Friedrichs fluxes near the opening fractures, where the density and pressure can be very low, with high-order monotonicity-preserving fluxes elsewhere. The fragmenting structure is discretized using a Discrete Element method based on particles, and fragmentation results from breaking the links between particles. The fluid-solid coupling is achieved by an Embedded Boundary method using a cut-cell Finite Volume method that ensures exact conservation of mass, momentum, and energy in the fluid. A time explicit approach is used for the computation of the energy and momentum transfer between the solid and the fluid. The Embedded Boundary method ensures that the exchange of fluid and solid momentum and energy is balanced. Numerical results are presented for two- and three-dimensional fragmenting structures interacting with shocked flows.