To prevent the uncontrolled development of a pathogenic biofilm around a dental implant, an antimicrobial drug-release electrospun membrane, set up between the implant and the gingival tissue, was developed by taking several technical, industrial and regulatory specifications into account. The membrane formulation is made of a blend of poly(l-lactic–co–gycolic acid) (PLGA, 85:15) and poly(l-lactic acide–co–ɛ-caprolactone) (PLC, 70:30) copolymers with chlorhexidine diacetate (CHX) complexed with β-cyclodextrin (CD). The amount of residual solvent, the mechanical properties and the drug release kinetics were tuned by the copolymers’ ratio, between 30% and 100% of PLC, and a CHX loading up to 20% w/w. The membranes were sterilized by γ-irradiation without significant property changes. The fiber′s diameter was between 600 nm and 3 µm, depending on the membrane composition and the electrospinning parameters. CHX was released in vitro over 10 days and the bacterial inhibitory concentration, 80 µg·mL−1, was reached within eight days. The optimal membrane, PGLA/PLC/CHX-CD (60%/40%/4%), exhibited a breaking strain of 50%, allowing its safe handling. This membrane and a membrane without CHX-CD were implanted subcutaneous in a rat model. The cell penetration remained low. The next step will be to increase the porosity of the membrane to improve the dynamic cell penetration and tissue remodeling.