This paper numerically investigates the microscopic damage in a single-fiber composite (SFC). A cohesive zone model (CZM) is presented to investigate the typical microscopic damages observed in the SFC. The CZM clarifies that the behavior of interfacial debonding, which influences significantly on the axial stress recovery of the embedded fiber, is greatly affected by matrix plasticity and cracking. We conduct a Monte-Carlo simulation for the fragmentation of the embedded fiber. The Monte-Carlo simulation demonstrates that these microscopic damages are important factors in the fragmentation of the embedded fiber. These simulated results are also compared with analytical models. These discussions reveal that the fragmentation process in an embedded fiber is controlled by the cohesive parameters of the fiber/matrix interface.