The study investigated the effect of dietary zinc glycine chelate and potato fibre on the absorption and utilisation of Zn, Cu, Fe, and Mn; the activity of Zn-containing enzymes (superoxide dismutase, SOD; alkaline phosphatase, ALP); and zinc transporter concentrations (metalothionein1, MT1; zinc transporter1, ZnT1) in tissues, with a special emphasis on the small intestine. Twenty-four barrows (Danbred × Duroc) were randomly allotted to four diets (supplemented with 10 g/kg of crude fibre and 120 mg Zn/kg) that consisted of cellulose and either zinc sulphate (C) or zinc glycinate (ZnGly), or contained potato fibre supplemented with ZnSO4 (PF) or ZnGly (PF + ZnGly). Feeding PF can influence the Zn absorption in the small intestine due to reduced zinc transporters MT1 and ZnT1 in the jejunum. The activity of antioxidant enzyme SOD and liver ZnT1, and duodenal iron concentrations were increased in the PF treatments. Dietary ZnGly did not significantly influence the Zn distribution, but it may alter the absorption of Fe and Mn. Given the elevated content of thiol groups and the Zn/Cu ratio in plasma, as well as the altered SOD activity and MT content in the tissues, we can conclude that feeding PF and ZnGly can influence the mineral and antioxidant status of growing piglets. However, further research is needed in order to elucidate the effect of both dietary sources on the transport systems of other minerals in enterocytes.