The aim of this study was to provide a beneficial treatment effect of mesenchymal stem cell products derived from the canine amniotic membrane (AM-MSC) on the complicated wound healing process in dogs. AM-MSCs were characterized in terms of morphology, phenotypic profile, and multilineage differentiation potential. The in vitro study of the effect of canine amniotic mesenchymal stem cell conditioned media (AMMSC-CM) on a primary skin fibroblast cell culture scratch assay showed a decrease in the measured scratch area of about 66.39% against the negative control (Dulbecco’s Modified Eagle’s Medium—32.55%) and the positive control (Dulbecco’s Modified Eagle’s Medium supplemented with FGF2, N2, B27, and EGF—82.077%) after 72 h treatment. In the experimental study, seven dogs with complicated nonhealing wounds were treated with a combination of antibiotics, NSAIDs, and local AMMSC-CM application. After 15 days of therapy, we observed a 98.47% reduction in the wound surface area as opposed to 57.135% in the control group treated by conventional therapy based on debridement of necrotic tissue, antibiotic therapy, pain management, and change of wound dressing.