Electrospinning is an effective method in preparing polymeric nanofibrous drug delivery systems (DDSs) for topical wound healing and skin burn therapy applications. The aim of the present study was to investigate a new synthetic graft copolymer (Soluplus) as a hydrophilic carrier polymer in electrospinning of nanofibrous DDSs. Soluplus (polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol graft copolymer (PCL-PVAc-PEG)) was applied in the nonwoven nanomats loaded with piroxicam (PRX) as a poorly water-soluble drug. Raman spectroscopy, X-ray powder diffraction, differential scanning calorimetry, and scanning electron microscopy (SEM) were used in the physical characterization of nanofibrous DDSs. According to the SEM results, the drug-loaded PCL-PVAc-PEG nanofibers were circular in cross-section with an average diameter ranging from 500 nm up to 2 µm. Electrospinning stabilized the amorphous state of PRX. In addition, consistent and sustained-release profile was achieved with the present nanofibrous DDSs at the physiologically relevant temperature and pH applicable in wound healing therapy. In conclusion, electrospinning can be used to prepare nanofibrous DDSs of PCL-PVAc-PEG graft copolymer (Soluplus) and to stabilize the amorphous state of a poorly water-soluble PRX. The use of this synthetic graft copolymer can open new options to formulate nanofibrous DDSs for wound healing.