The Genus Mycobacterium includes pathogens known to cause disease in mammals such as tuberculosis (Mycobacterium tuberculosis) and skin infections (M. abscessus). M. smegmatis is a model bacterium that can cause opportunistic infections in human tissues and, rarely, a respiratory disease. Due to the emergence of multidrug-resistant bacteria, phage therapy is potentially an alternative way of treating these bacterial infections. As bacteriophages are specific to their bacterial host, it ensures that the normal flora is unharmed. Fulbright is a mycobacteriophage that infects the host bacteria M. smegmatis. The main goal of this study is to incorporate Mycobacteriophage Fulbright into a polycaprolactone (PCL) nanofiber and test its antimicrobial effect against the host bacteria, M. smegmatis. Stability tests conducted over 7 days showed that the phage titer does not decrease when in contact with PCL, making it a promising vehicle for phage delivery. Antimicrobial assays showed that PCL_Fulbright effectively reduces bacterial concentration after 24 h of contact. In addition, when stored at −20 °C, the phage remains viable for up to eleven months in the fiber. Fulbright addition on the nanofibrous mats resulted in an increase in water uptake and decrease in the mechanical properties (strength and Young’s modulus) of the membranes, indicating that the presence of phage Fulbright can greatly enhance the physical and mechanical properties of the PCL. Cytotoxicity assays showed that PCL_Fulbright is not cytotoxic to Balbc/3T3 mouse embryo fibroblast cell lines; thus, phage-incorporated PCL is a promising alternative to antibiotics in treating skin infections.