Here, we studied the self-healing of composite materials filled with epoxy-containing nanofibers. An initial incision in the middle of a composite sample stretched in a static fatigue test can result in either crack propagation or healing. In this study, crack evolution was observed in real time. A binary epoxy, which acted as a self-healing agent, was encapsulated in two separate types of interwoven nano/microfibers formed by dual-solution blowing, with the core containing either epoxy or hardener and the shell being formed from poly(vinylidene fluoride)/ poly(ethylene oxide) mixture. The core-shell fibers were encased in a poly(dimethylsiloxane) matrix. When the fibers were damaged by a growing crack in this fiber-reinforced composite material because of static stretching in the fatigue test, they broke and released the healing agent into the crack area. The epoxy used in this study was cured and solidified for approximately an hour at room temperature, which then conglutinated and healed the damaged location. The observations were made for at least several hours and in some cases up to several days. It was revealed that the presence of the healing agent (the epoxy) in the fibers successfully prevented the propagation of cracks in stretched samples subjected to the fatigue test. A theoretical analysis of subcritical cracks was performed, and it revealed a jumplike growth of subcritical cracks, which was in qualitative agreement with the experimental results.