Materials and scaffolds with antimicrobial properties are of great importance in would dressing and other tissue engineering applications. The objective of the present work was to fabricate scaffolds made from nanocomposites of polycaprolactone (PCL) and quaternary ammonium salt-modified montmorillonite (MMT) by the electrospinning technique, and then characterize their antimicrobial and other properties for wound dressing applications. The effect of MMT on the structure, morphology, and thermal behavior of the electrospun wound dressings was assessed by means of X-ray diffraction (XRD), thermogravimetric analysis (TGA), and scanning electron microscopy (SEM); the swelling capacity, antibacterial activity, and cytotoxicity were also evaluated. The results of XRD and SEM analyses showed MMT was successfully incorporated into the PCL polymeric matrix and its inclusion reduced the size and thickness of the electrospun fibers compared to pure PCL fibers. The TGA results illustrated an increase in the thermal stability of nanocomposites upon incorporation of nano clay into the PCL matrix. The swelling capacity of the wound dressings was reduced by increasing the amount of MMT in the PCL matrix due to the increased hydrophobicity of the original MMT resulting from its modification with quaternary ammonium salt. The curcumin (Cur) release profile revealed an initial burst release followed by a sustained release, with the burst release level reduced by the introduction of MMT into the polymeric matrix. Increasing the nano clay content further reduced the curcumin release, with the PCL/20%MMT/Cur dressings having the lowest curcumin release of all those tested. The beneficial effect of MMT on the antibacterial behavior of electrospun wound dressings based on PCL/MMT nanocomposites was confirmed, with the introduction of both MMT and curcumin into the PCL matrix resulting in lower bacterial viability. PCL/10%MMT/Cur demonstrated higher antimicrobial activity and the greatest bacterial colony reduction compared to both pure PCL and PCL/10%MMT. The cytotoxicity evaluation indicated low toxicity and confirmed the potential of PCL/MMT nanocomposite scaffolds for wound dressing applications.