In cases of injury to the skin tissue, such as severe burns, these layers can be extensively damaged. A variety of dressings have been developed to address different types of wounds, with functional polymeric dressings being among the most popular. These advanced dressings are designed to accelerate the wound-healing process. The incorporation of plant-derived extracts and biological molecules into wound dressing materials is a common practice. This study aimed to develop an electrospun nanofiber wound dressing by incorporating active ingredients extracted from the plant Echium italicum (Italian viper's bugloss), known for its efficacy in burn wound healing, into poly(lactic-co-glycolic acid) (PLGA). The nanofiber membrane wound dressings produced by electrospinning were subjected to various analyses. Morphological and structural characterization revealed that the membranes exhibited significant morphological decomposition and weight loss after 90 days of in vitro degradation under physiological conditions. In vitro cytotoxicity testing, conducted using the MEM extraction method, demonstrated that the membranes were not cytotoxic. Based on the comprehensive analysis, it was concluded that the developed nanofiber membranes hold promise as potential wound dressings for the treatment of severe burn wounds.