Surgical sutures designed to prevent infection are critical in addressing antibiotic-resistant pathogens that cause surgical site infections. Instead of antibiotics, alternative materials such as biocides have been assessed for coating commercially used sutures due to emerging antibiotic resistance concerns worldwide. This study has a new approach to the development of fibrous surgical sutures with the ability to deliver localized antibacterial agents. A new manufacturing process based on pressure spinning was used for the first time in the production of fibrous surgical sutures by physically blending antibacterial triclosan (Tri) agent with poly(lactic-co-glycolic acid) (PLGA) and poly(ethylene oxide) (PEO) polymers. Fibrous surgical sutures with virgin PLGA, virgin PEO, different ratios of PLGA-PEO, and different ratios of Tri-loaded PLGA-PEO fibrous sutures were produced to mimic the FDA- and NICE-approved PLGA-based sutures available in the market and compared for their characteristics. They were also tested simultaneously with commercially available sutures to compare their in vitro biodegradation, antibacterial, drug release, and cytotoxicity properties. After in vitro antibacterial testing for 24 h, sutures having 285 ± 12 μg/mg Tri loading were selected as a model for further testing as they exhibited antibacterial activity against all tested bacteria strains. The selected model of antibacterial fibrous sutures exhibited an initial burst of Tri release within 24 h, followed by a sustained release for the remaining time until the sutures completely degraded within 21 days. The cell viability assay showed that these surgical sutures had no cytotoxic effect on mammalian cells.