The fabrication of biodegradable, bioabsorbable, and biocompatible vascular scaffolds with enhanced mechanical and biological properties that are able to modulate local inflammation and induce endothelialization after surgical implant is still a challenge. In this work, a fibrous scaffold, made of poly(ε-caprolactone) and poly(glycerol sebacate), was fabricated to be potentially used as a small-diameter graft in vascular surgery. The novelty of this research is represented by the direct incorporation of quercetin, a well-known antioxidant compound with several biological properties, into a polymeric scaffold obtaining a vascular construct able to modulate two key factors involved in postsurgical inflammation, matrix metalloproteinase-9 and endothelial nitric oxide synthase. For its production, an electrospinning apparatus, a solution made of the two polymers (both 20% (w/v), mixed at the ratio 1:1 (v/v)), and free quercetin (0.05% (w/v)) were used. Scanning electron and atomic force microscopies were employed to investigate the morphological properties of the fabricated electrospun scaffolds. Furthermore, physicochemical properties, including Fourier-transform infrared spectroscopy, mass loss, fluid uptake, quercetin release, mechanical properties, and biological activity of the scaffolds were studied. The expression of matrix metalloproteinase-9, tissue inhibitor of metalloproteinase-1, and of endothelial nitric oxide synthase was evaluated when the quercetin-functionalized scaffold was exposed to human endothelial cells treated with tumor necrosis factor-α. The results of this study confirmed the feasibility of incorporating free quercetin during the electrospinning process to impart biological properties to small-diameter vascular prostheses.