The umbilical cord is a material that enhances regeneration and is devoid of age-related changes in the extracellular matrix (ECM). The aim of this work was to develop a biodegradable scaffold from a decellularized human umbilical cord (UC-scaffold) to heal full-thickness wounds. Decellularization was performed with 0.05% sodium dodecyl sulfate solution. The UC-scaffold was studied using morphological analysis methods. The composition of the UC-scaffold was studied using immunoblotting and Fourier transform infrared spectroscopy. The adhesion and proliferation of mesenchymal stromal cells were investigated using the LIVE/DEAD assay. The local reaction was determined by subcutaneous implantation in mice (n = 60). A model of a full-thickness skin wound in mice (n = 64) was used to assess the biological activity of the UC-scaffold. The proposed decellularization method showed its effectiveness in the umbilical cord, as it removed cells and retained a porous structure, type I and type IV collagen, TGF-β3, VEGF, and fibronectin in the ECM. The biodegradation of the UC-scaffold in the presence of collagenase, its stability during incubation in hyaluronidase solution, and its ability to swell by 1617 ± 120% were demonstrated. Subcutaneous scaffold implantation in mice showed gradual resorption of the product in vivo without the formation of a dense connective tissue capsule. Epithelialization of the wound occurred completely in contrast to the controls. All of these data suggest a potential for the use of the UC-scaffold.