Fibrous membranes based on natural polymers obtained by the electrospinning technique are a great choice for wound dressings. In order to promote an efficient wound repair, and to avoid antibiotics, antibacterial plant extracts can be incorporated. In the present work, the new electrospun nanofibre membranes based on monobasic phosphate curdlan (PCurd) and polyvinyl alcohol (PVA) were obtained for the first time. To establish the adequate mixing ratio for electrospinning, the behaviour of the PCurd and PVA mixture was studied by viscometry and rheology. In order to confer antimicrobial activity with the nanofibre membrane, clove essential oil (CEO) was incorporated into the electrospun solution. Well-defined and drop-free nanofibres with a diameter between 157 nm and 110 nm were obtained. The presence of CEO in the obtained nanofibres was confirmed by ATR–FTIR spectroscopy, by the phenolic and flavonoid contents, and by the antioxidant activity of the membranes. In physiological conditions, CEO was released from the membrane after 24 h. The in vivo antimicrobial tests showed a good inhibitory activity against E. coli and higher activity against S. aureus. Furthermore, the viability cell test showed the lack of cytotoxicity of the nanofibre membrane with and without CEO, confirming its potential use in wound treatment.