Appropriately adapted comprehensive mechanical properties, degradation behavior and biocompatibility are prerequisites for the application of Zn-based biodegradable implants. In this study, hot-extruded Zn–0.5Cu–xFe (x = 0.1, 0.2 and 0.4 wt%) alloys were fabricated as candidates for biodegradable materials for guided bone regeneration (GBR) membranes. The hot-extrusion process and Cu alloying were expected mostly to enhance the mechanical properties, and the Fe alloying was added mainly for regulating the degradation. The microstructure, mechanical properties and in vitro degradation behavior were systematically investigated. The ZnCuFe alloys were composed of a Zn matrix and FeZn13 phase. With increasing Fe content, a higher FeZn13 phase precipitation with larger particles was observed. Since elongation declined significantly until fracture with increasing Fe content up to 0.4 wt%, the ZnCuFe (0.2 wt%) alloy achieved a good balance between mechanical strength and ductility, with an ultimate tensile strength of 202.3 MPa and elongation at fracture of 41.2%. Moreover, the addition of Fe successfully accelerated the degradation of ZnCuFe alloys. The ZnCuFe (0.2 wt%) alloy showed relatively uniform corrosion in the long-term degradation test. Furthermore, extracts of the ZnCuFe (0.2 wt%) alloy showed no apparent cytotoxic effects against L929 fibroblasts, Saos-2 osteoblasts or TAg periosteal cells. The ZnCuFe (0.2 wt%) alloy exhibited the potential to inhibit bacterial adhesion of Streptococcus gordonii and mixed oral bacteria. Our study provides evidence that the ZnCuFe (0.2 wt%) alloy can represent a promising material for the application as a suitable GBR membrane.