This work describes the development of a fully three-dimensional coupled geomechanics and multiphase flow formulation to model the dynamic propagation of injection-induced fractures. A dynamic filtration model for permeability reduction is employed on the fracture to incorporate effects of internal damage and external filter cake build-up due to solids injection. The formulation is based on a finite volume implementation of the cohesive zone model for arbitrary fracture propagation coupled with multiphase flow, for multiple injection wells and fractures. Uniform, anisotropic stresses are considered in a poro-thermo-elastic reservoir domain. This is the first instance where a finite volume formulation of multiphase flow in the reservoir has been coupled with dynamic fracture propagation induced by solids plugging, in a poro-thermo-elastic domain.