The aim of the study was to assess the potential of milk from herbal blend-fed cows to be used for the production of yogurts exhibiting increased antioxidant potential with regard to the duration of refrigerated storage of the products. Bulk milk (control—CM and experimental—EM) intended for the production of yogurts was provided by a dairy cattle breeding farm. The milk samples were analyzed to determine their basic chemical composition (the content of dry matter, fat, and total protein including casein), hygienic status (somatic cell count (SCC) and total microbial count (TMC)), and antioxidant activity (FRAP, DPPH, and ABTS assays). Pasteurized milk was used to manufacture natural yogurts with the use of starter cultures YC-X11 (Chr. Hansen, Hørsholm, Denmark). Changes in physicochemical traits (acidity, nutritional value, and water activity) and antioxidant activity (FRAP, DPPH, and ABTS assays) occurring during 21-day refrigerated storage of the yogurts were determined. The analyses revealed that the yogurts had higher antioxidant potential than the milk, irrespective of the determination method. Additionally, the experimental yogurts produced from milk obtained from the cows fed fodder supplemented with an herbal mixture exhibited significantly higher antioxidant activity than the control yogurts. The antioxidant potential of the yogurts changed during the refrigerated storage. It should be emphasized that their antioxidant activity significantly increased during the first two weeks (until day 14) but decreased by 15–20% in the following week.