For the effective management of infected chronic wounds, the incorporation of antimicrobial drugs into wound dressings can increase their local availability at the infection site. Mesoporous silicon dioxide SBA-15 is an excellent drug carrier with tunable drug release kinetics. In this work, synthesized SBA-15 loaded with the natural antimicrobial compound thymol (THY) was incorporated into polycaprolactone (PCL) electrospun nanofibers to obtain an advanced wound dressing. Rod-shaped particles with internal parallel channels oriented along the longitudinal axis (diameter: 138 ± 30 nm, length: 563 ± 100 nm) were loaded with 70.8 wt.% of THY. Fiber mats were prepared using these particles as nanofillers within polycaprolactone (PCL) electrospun fibers. The resulting mats contained 5.6 wt.% of THY and more than half of this loading was released in the first 7 h. This release would prevent an initial bacterial colonization and also inhibit or eliminate bacterial growth as in vitro shown against Staphylococcus aureus ATCC 25923. Minimal inhibitory concentration (MIC: 0.07 mg/mL) and minimal bactericidal concentration (MBC: 0.11 mg/mL) of released THY were lower than the amount of free THY required, demonstrating the benefit of drug encapsulation for a more efficient bactericidal capacity due to the direct contact between mats and bacteria.