Opportunistic skin pathogens and their resistance to pre-existing therapeutics are a challenge to normal physiological wound healing processes. Consistent development of antimicrobial agents is required to overcome the complications raised by antimicrobial resistance. An effective alternative proposed in recent research includes the use of antimicrobial nanoparticles or nanobiopolymers. Unfortunately, metallic nanoparticles that have been proven as antimicrobial agents also possess a certain level of toxicity. In this work, we demonstrate the use of a cationic polymer, branched polyethyleneimine (B-PEI), that has been electrospun to obtain a scaffold/fiber (B-PEI NF) mat resulting in a large surface area-to-volume ratio. SEM analysis revealed that the average diameter of the obtained fibers is 240 nm. The formation of nanoscaffold modulates the controlled release of the polymer from the matrix resulting in long-term effects. The antimicrobial and antibiofilm activity of the B-PEI nanofiber (B-PEI NF) was evaluated against ESKAPE pathogens (Pseudomonas aeruginosa and Staphylococcus aureus) and also against Candida albicans. Dose-dependent inhibition was observed for microbial growth and biofilm for all three test organisms, the minimum inhibitory concentration required for inhibiting P. aeruginosa, S. aureus, and C. albicans is 33.125, 26.5, and 19.875 μM, respectively, in 2 mL of bacterial/fungal broth. Crystal violet and 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assays showed significant reduction in biomass and cell viability of sessile cells, respectively, within the biofilm after treatment using B-PEI NFs. A B-PEI NF matrix promotes cell migration and wound healing processes by mimicking the extracellular matrix. In vitro wound healing studies showed a fivefold increase in cell migration and wound healing by B-PEI NFs (97% wound coverage in 17 h) when compared to B-PEI (15% wound coverage in 17 h). The in vitro wound healing assays confirmed the biocompatibility and better wound healing activity of B-PEI NF mats.