The main goal of this study was to develop poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) films with long-term antimicrobial capacity of interest in food packaging applications. To this end, eugenol was first highly efficiently encapsulated at 50 wt.-% in the pores of mesoporous silica nanoparticles by vapor adsorption. The eugenol-containing nanoparticles were then loaded in the 2.5–20 wt.-% range into PHBV by electrospinning and the resultant electrospun composite fibers were annealed at 155 °C to produce continuous films. The characterization showed that the PHBV films filled with mesoporous silica nanoparticles containing eugenol present sufficient thermal resistance and enhanced mechanical strength and barrier performance to water vapor and limonene. The antimicrobial activity of the films was also evaluated against foodborne bacteria for 15 days in open vs. closed conditions in order to simulate real packaging conditions. The electrospun PHBV films with loadings above 10 wt.-% of mesoporous silica nanoparticles containing eugenol successfully inhibited the bacterial growth, whereas the active films stored in hermetically closed systems increased their antimicrobial activity after 15 days due to the volatile portion accumulated in the system’s headspace and the sustained release capacity of the films. The resultant biopolymer films are, therefore, potential candidates to be applied in active food packaging applications to provide shelf life extension and food safety.