Voids are representative of the damage process in both creep and ductile fractures. Although the matrix/precipitate interface has been considered the preferential nucleation site for voids, the relationship between the atomic structure of this interface and the nucleation mechanism of a void has never been sufficiently investigated. In this study, the bcc Fe/V4C3 interface is selected as a model interface between a matrix and precipitate. The vacancy formation energy and intrinsic mechanical strength at this interface are investigated using a first-principles calculation because they should be related with the nucleation of creep and ductile voids, respectively. Within the considered interface, the Fe vacancy is found to be dominant. When the Baker-Nutting orientation relationship is satisfied at the interface, the calculated intrinsic mechanical strength of the interface is 23.8 GPa. However, when the geometric coherence at the interface is low as compared to that of the Baker-Nutting orientation relationship, it is found that the interfacial mechanical strength is significantly weakened. At each interface, it is found that the back-bond of the interface determined the interfacial strength because of the strongly bonded Fe-C on the interface. The nucleation mechanism of a void at the matrix/precipitate interface is discussed based on the present findings. It is suggested that local decohesion at the matrix/precipitate interface should be the origin of the nucleation of a ductile void.