Wounds are characterised by an anatomical disruption of the skin; this leaves the body exposed to opportunistic pathogens which contribute to infections. Current wound healing bandages do little to protect against this and when they do, they can often utilise harmful additions. Historically, plant-based constituents have been extensively used for wound treatment and are proven beneficial in such environments. In this work, the essential oil of clove bud (Syzygium aromaticum) was incorporated in a polycaprolactone (PCL) solution, and 44.4% (v/v) oil-containing fibres were produced through pressurised gyration. The antimicrobial activity of these bandage-like fibres was analysed using in vitro disk diffusion and the physical fibre properties were also assessed. The work showed that advantageous fibre morphologies were achieved with diameters of 10.90 ± 4.99 μm. The clove bud oil fibres demonstrated good antimicrobial properties. They exhibited inhibition zone diameters of 30, 18, 11, and 20 mm against microbial colonies of C. albicans, E. coli, S. aureus, and S. pyogenes, respectively. These microbial species are commonly problematic in environments where the skin barrier is compromised. The outcomes of this study are thus very promising and suggest that clove bud oil is highly suitable to be applied as a natural sustainable alternative to modern medicine.