Wound healing has grown to be a significant problem at a global scale. The lack of multifunctionality in most wound dressing-based biopolymers prevents them from meeting all clinical requirements. Therefore, a multifunctional biopolymer-based tri-layered hierarchically nanofibrous scaffold in wound dressing can contribute to skin regeneration. In this study, a multifunctional antibacterial biopolymer-based tri-layered hierarchically nanofibrous scaffold comprising three layers was constructed. The bottom and the top layers contain hydrophilic silk fibroin (SF) and fish skin collagen (COL), respectively, for accelerated healing, interspersed with a middle layer of hydrophobic poly-3-hydroxybutyrate (PHB) containing amoxicillin (AMX) as an antibacterial drug. The advantageous physicochemical properties of the nanofibrous scaffold were estimated by SEM, FTIR, fluid uptake, contact angle, porosity, and mechanical properties. Moreover, the in vitro cytotoxicity and cell healing were assessed by MTT assay and the cell scratching method, respectively, and revealed excellent biocompatibility. The nanofibrous scaffold exhibited significant antimicrobial activity against multiple pathogenic bacteria. Furthermore, the in vivo wound healing and histological studies demonstrated complete wound healing in wounded rats on day 14, along with an increase in the expression level of the transforming growth factor-β1 (TGF-β1) and a decrease in the expression level of interleukin-6 (IL-6). The results revealed that the fabricated nanofibrous scaffold is a potent wound dressing scaffold, and significantly accelerates full-thickness wound healing in a rat model.