Wound healing, one of the most complex processes of the body involving the cooperation of several important biomolecules and pathways, is one of the major therapeutic and economic issues in regenerative medicine. The present study aimed to introduce a novel electrospun curcumin (Cur)‐incorporated chitosan/polyvinyl alcohol/carbopol/polycaprolactone nanofibrous composite for concurrent delivery of the buccal fat pad‐derived mesenchymal stem cells (BFP‐MSCs) and Cur to a full‐thickness wound on the mouse model. Scaffolds were characterized structurally using scanning electron microscopy (SEM), fluorescence microscopy imaging and Fourier‐transform infrared spectroscopy, and toxicity of the scaffolds was also evaluated after BFP‐MSC seeding by SEM imaging and 3‐(4,5 dimethyiazol‐2‐1)‐2‐5‐diphenyl tetrazolium bromide (MTT) assay. Then, its influence on the wound‐healing process was investigated as a wound dressing for a full‐thickness skin defect in mouse model. Results demonstrated that the designed composite scaffolds have the capability for cell seeding and support their growth and proliferation. Macroscopic and histopathological characteristics were evaluated at the end of the 7 and 14 days after surgery, and their results showed that our designed scaffold groups accelerated the wound‐healing process compared with the control group. Among those, scaffold/Cur, scaffold/Cur/BFP‐MSC and scaffold/BFP‐MSC groups demonstrated more wound repair efficacy. These results indicated that the combined grafts can be used to improve the wound‐healing process, and therefore, the electrospun nanofibers presented in this study, Cur and BFP‐MSC together, were demonstrated to have promising potential for wound‐dressing applications.