The study is concerned with the mechanical properties of Zn and three Zn–Mg double alloys with Mg concentrations: 0.5%, 1.0% and 1.5% in the form of rods with a diameter of 5 mm as potential materials for use in biodegradable medical implants, such as vascular stents. The materials were cast, next conventionally hot extruded at 250 °C and finally, hydrostatically extruded (HE) at ambient temperature. Occasionally HE process was carried at liquid nitrogen temperature or in combination with the ECAP process. After HE, the microstructure of the alloys was made up of fine-grained αZn of mean grain size ~1 μm in a 2-phase coat of 50–200 nm nano-grains of the fine αZn + Mg2Zn11 eutectic. The 3 to 4-fold reduction of grain size as a result of HE allowed an increase in yield strength from 100% to over 200%, elongation to fracture from 100% to thirty fold and hardness over 50% compared to the best literature results for similar alloys. Exceptions accounted for elongation to fracture in case of Zn-0.5 Mg alloy and hardness in case of Zn-1.5 Mg alloy, both of which fell by 20%. For the Zn-0.5 Mg and Zn–1Mg alloys, after immersion tests, no corrosive degradation of plasticity was observed. Achieving these properties was the result of generating large plastic deformations at ambient temperature due to the application of high pressure forming with the cumulative HE method. The results showed that Zn–Mg binary alloys after HE have mechanical and corrosive characteristics, qualifying them for applications in biodegradable implants, including vascular stents.