It is known that zinc biodegradable alloys are a promising material for producing biomedical implants for orthopedics and vascular stents. Among them, the Zn-Ag-Cu zinc alloy is of special interest due to the antibacterial and antimicrobial properties of Ag and Cu. To improve the mechanical properties of the Zn-4Ag-1Cu zinc alloy, the effect of equal-channel angular pressing (ECAP) on the microstructure and strength has been investigated. The ECAP conditions for the Zn-4Ag-1Cu alloy were chosen by modeling in the Deform 3 D program (temperature and strain rate). The microstructure was analyzed using transmission electron microscopy, scanning electron microscopy and X-ray diffraction analysis. The study of strength was carried out by measuring the microhardness and tensile tests of small samples with a gauge dimension of 0.8 × 1 × 4 mm3. The microstructure after ECAP was characterized by equiaxed grains ranging in a size from 1.5 µm to 4 µm with particles in a size from 200 nm to 1 µm uniformly distributed along the boundaries. The ECAP samples showed a high strength of 348 MPa and good ductility of up to 30%, demonstrating their great potential as promising materials for producing medical stents.