In a previous study, we developed electrospun antimicrobial microfiber scaffolds for wound healing composed of a core of zein protein and a shell containing polyethylene oxide. While providing a promising platform for composite nanofiber design, the scaffolds showed low tensile strengths, insufficient water stability, as well as burst release of the antimicrobial drug tetracycline hydrochloride, properties which are not ideal for the use of the scaffolds as wound dressings. Therefore, the aim of the present study was to develop fibers with enhanced mechanical strength and water stability, also displaying sustained release of tetracycline hydrochloride. Zein was chosen as core material, while the shell was formed by the hydrophobic polymer polycaprolactone, either alone or in combination with polyethylene oxide. As compared to control fibers of pristine polycaprolactone, the zein-polycaprolactone fibers exhibited a reduced diameter and hydrophobicity, which is beneficial for cell attachment and wound closure. Such fibers also demonstrated sustained release of tetracycline hydrochloride, as well as water stability, ductility, high mechanical strength and fibroblast attachment, hence representing a step towards the development of biodegradable wound dressings with prolonged drug release, which can be left on the wound for a longer time.