Self-healing materials science has seen significant advances in the last decade. Recent efforts have demonstrated healing in polymeric materials through chemical reaction, thermal treatment, and ultraviolet irradiation. The existing technology for healing polymeric materials through the aforementioned mechanisms produces an irreversible change in the material and makes it unsuitable for subsequent healing cycles. To overcome these disadvantages, we demonstrate a new composite self-healing material made from an ionomer (Surlyn) and carbon fiber that can sustain damage from medium-velocity impact and heal from the energy of the impact. Furthermore, the carbon fiber embedded in the polymer matrix results in resistive heating of the polymer matrix locally, melts the ionomer matrix around the damage, and heals the material at the damaged location. This paper presents methods to melt-process Surlyn with carbon fiber and demonstrates healing in the material through medium-velocity impact tests, resistive heating, and imaging through electron and optical microscopy. A new metric for quantifying self-healing in the sample, called width-heal ratio, is developed, and we report that the Surlyn-carbon fiber-based material under an optimal rate of heating and at the correct temperature has a width-heal ratio of >0.9, thereby demonstrating complete recovery from the damage.