The study was carried out to evaluate the effect of Zn-Gly supplementation on the selected antioxidative enzymes and on the mineral composition in the liver and faeces as well as the biochemical and haematological parameters of chicken blood. Two hundred and fifty-one-day-old Ross 308 male broiler chicks were randomly allotted to five dietary treatments, each of which was replicated five times (10 birds in each cage). Five experimental groups were formed: control negative (CN)—without Zn, control positive supplemented with 100 mg ZnO, and three groups supplemented with 100, 50, and 25 mg Zn-Gly. An increase (P < 0.05) was recorded in the concentration of Cu and Zn in chicken livers after Zn-Gly supplementation, irrespective of the level of supply with the diet. The addition of 100 mg·Zn-Gly improved the activity of SODCuZn (P < 0.05) and reduced the MDA value (P < 0.05) in chicken livers. The addition of 100, 50, and 25 mg Zn-Gly reduced the concentration of zinc in the birds’ droppings, compared to the CN and 100 mg ZnO group. Zn-Gly at the level of 50 mg increased the concentration of Cu and Ca in chicken blood. The results indicate that the addition of Zn-Gly increased the antioxidative capacity of the body and storage of Zn and Cu in the liver; it also reduced the amount of Zn excreted with faeces. Zn-Gly can be an alternative to ZnO in providing a good source of Zn to enrich feed mixtures for broilers.