Preventing infections is one of the main focuses of wound care. The colonisation of wounds by microorganisms can in fact have negative consequences on the healing process, delaying it. Here, we propose the use of essential oils as natural antimicrobial agents for cellulose-based fibrous dressings. We demonstrate the production of composite electrospun fibres that effectively encapsulate three different types of essential oils (cinnamon, lemongrass and peppermint). The fibrous scaffolds are able to inhibit the growth of Escherichia coli, even when small amounts of essential oils were used. At the same time, they are not cytotoxic, as proved by biocompatibility assays on skin cell models. The created dressings are promising as advanced biomedical devices for topical treatments.