In recent years, increasing interest has been placed in the development of Zn alloys for absorbable biomedical applications. It has been demonstrated that these alloys are potential candidates for endovascular applications. In the present work, a novel Zn-12.5Ag-1Mg alloy was investigated as a potential biomedical absorbable material. As a reference, the exhibited biocompatible properties are compared with those of pure Zn and a Zn-1Mg alloy. All the alloys investigated in this work were cast in a water-cooled Cu-mold (chill casting). Subsequently, the alloys were solution-treated and then extruded. The microstructural evolution at each stage of the alloy processing was resolved by analytical means including optical, scanning, transmission microscopy, and X-ray diffraction. By these means, the various phases belonging to this alloy system were disclosed. In addition, determinations of both corrosion and mechanical properties were carried out in the proposed Zn-12.5Ag-1Mg alloy. In particular, an excellent combination of strength and ductility was found, which is attributed to grain refinement as well as the precipitation of a uniform distribution of refined phases (i.e., AgZn solid solution, ε-AgZn3, and Ag0.15MgZn1.85 intermetallics). All the precipitated intermetallics were embedded in a η-Zn matrix. As for the corrosion degradation in the physiological NaCl solution in the as-extruded condition, the experimental outcome indicates that the Zn-12.5Ag-1Mg alloy exhibits degradation rates far superior to currently reported ones for Zn-based alloys intended for absorbable biomedical applications.