Wound healing is a complex and costly public health problem that should be timely addressed to achieve a rapid and adequate tissue repair avoiding or even eliminating potential pathogenic infection. Chronic infected non-healing wounds represent a serious concern for health care systems. Efficient wound dressings with tailored therapy having the best response and highest safety margin for the management of chronic non-healing wounds are still needed. The use of novel wound dressing materials has emerged as a promising tool to fulfil these requirements. In this work, asymmetric electrospun polycaprolactone (PCL)-based nanofibers (NFs) were decorated with electrosprayed poly(lactic-co-glycolic acid) microparticles (PLGA MPs) containing the natural antibacterial compound thymol (THY) in order to obtain drug eluting antimicrobial dressings having sustained release. The synthesized dressings successfully inhibited the in vitro growth of Staphylococcus aureus ATCC 25923, showing also at the same doses cytocompatibility on human dermal fibroblasts and keratinocyte cultures after treatment for 24 h, which was not observed when using free thymol. An in vivo murine excisional wound splinting model, followed by the experimental infection of the wounds with S. aureus and their treatment with the synthesized dressings, pointed to the reduction of the bacterial load in wounds after 7 days, though the total elimination of the infection was not reached. The findings indicated the relevance of the direct contact between the dressings and the bacteria, highlighting the need to tune their design considering the wound surface and the nature of the antimicrobial cargo contained.