This work focuses on the manufacture of core-sheath nanofibers (NFs) based on chitosan (CHT) as sheath and cyclodextrin polymer (PCD) as core and loaded with triclosan (TCL). In parallel, monolithic NFs consisting of blended CHT-PCD and TCL were prepared. Nanofibers were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Fourier Transform Infrared spectroscopy (FTIR). SEM displayed the morphology of NFs and the structure of the nanowebs, while TEM evidenced the core-sheath structure of NFs prepared by coaxial electrospinning. The core diameters and sheath thicknesses were found dependent on respective flow rates of both precursor solutions. Nanofibers stability and TCL release in aqueous medium were studied and correlated with the antibacterial activity against Staphylococcus aureus and Escherichia coli. Results showed that the release profiles of TCL and therefore the antibacterial activity were directly related to the type of nanofibers. In the case of monolithic nanofibers, the NFs matrix was composed of polyelectrolyte complex (PEC formed between CHT and PCD) and resulted in a prolonged release of TCL and a sustained antibacterial effect. In the case of core-sheath NFs, the PEC was formed only at the core-sheath interface, leading to less stable NFs and therefore to a faster release of TCL, and to a less extended antibacterial activity compared to monolithic ones.