The use of electrospun fibers as anti-inflammatory drug carriers is currently one of the most interesting approaches for the design of drug delivery systems. In recent years, biodegradable polymers blended with naturally derived ones have been extensively studied to fabricate bioinspired platforms capable of driving biological responses by releasing selected molecular/pharmaceutical signals. Here, sodium diclofenac (DicNa)-loaded electrospun fibers, consisting of polycaprolactone (PCL) or gelatin-functionalized PCL, were studied to evaluate fibroblasts' in vitro and in vivo response. In vitro studies demonstrated that cell adhesion of L929 cells (≈70%) was not affected by the presence of DicNa after 4 h. Moreover, the initial burst release of the drug from PD and PGD fibers, e.g., 80 and 48%, respectively, after 5 h-combined with its sustained release-did not produce any cytotoxic effect and did not negatively influence the biological activity of the cells. In particular, it was demonstrated that the addition of gelatin concurred to slow down the release mechanism, thus limiting the antiproliferative effect of DicNa, as confirmed by the significant increase in cell viability and collagen deposition after 7 days, with respect to PCL alone. In vivo studies in a rat subcutaneous model also confirmed the ability of DicNa-loaded fibers to moderate the inflammatory/foreign body response independently through the presence of gelatin that played a significant role in supporting the formation of small-caliber vessels after 10 days of implantation. All of these results suggest using bicomponent fibers loaded with DicNa as a valid therapeutic tool capable of supporting the wound healing process and limiting in vivo inflammation and rejection phenomena.