High-quality and aesthetic wound healing, as well as effective medical support of this process, continue to be relevant. This study aims to evaluate the medical efficacy of a novel smart polymeric nanodrug (SPN) on the rate and mechanism of wound healing in experimental animals. The study was carried out in male Wistar rats (aged 8–9 months). In these animals, identical square wounds down to the fascia were made in non-sterile conditions on the back on both sides of the vertebra. SPN was used for the treatment of one wound, and the other wound was left without treatment (control group). Biocompatible citrate-stabilized cerium oxide nanoparticles integrated into a polysaccharide hydrogel matrix containing natural and synthetic polysaccharide polymers (pectin, alginate, chitosan, agar-agar, water-soluble cellulose derivatives) were used as the therapeutic agent. Changes in the wound sizes (area, volume) over time and wound temperature were assessed on Days 0, 1, 3, 5, 7, and 14. Histological examination of the wounds was performed on Days 3, 7, and 14. The study showed that the use of SPN accelerated wound healing in comparison with control wounds by inhibiting the inflammatory response, which was measured by a decreased number of white blood cells in SPN-treated wounds. It also accelerated the development of fibroblasts, with an early onset of new collagen synthesis, which eventually led to the formation of more tender postoperative scars. Thus, the study demonstrated that the use of SPN for the treatment of wounds was effective and promising.