Diabetic wounds are instantaneously prone to the bacterial infections that can delay healing process. An efficient wound dressing material is critical to a fast healing of wounds in diabetic patients. The present study focuses on the synthesis of the yeast extract (YE)-immobilized and copper (Cu) nanoparticle (NP)-dispersed carbon nanofibers (CNFs) as a potential diabetic wound dressing material. The biological assays, namely, platelet aggregation, hemolysis, cells viability, and proliferation of macrophage cells show the prepared biomaterial to be noncytotoxic. Chemical tests performed on the material show a significant consumption of glucose, whereas the antibacterial tests show the material to be efficiently inhibiting the E. coli and S. aureus strains, ascribed to the antibacterial characteristics of the immobilized YE and the dispersed Cu-NPs, respectively, in the CNFs. To analyze the in vivo wound healing property, a 1 cm circular full thickness skin wound was created in diabetic Wistar rats. The wounds with dressings showed enhanced healing rate compared to those in the control animals (without dressing). Maximum healing (wound closure) was observed in the Cu-CNF-YE (95%) group, followed by Cu-CNF (94%), activated carbon micronanofibers (ACF-CNF) (87%), and control animals with only 74% healing. The method of preparing Cu-CNF-YE metal-enzyme-fabric described in this study is facile, and the composite can be applied as an effective dressing material for diabetic wounds.