Blackcurrant ( L.) is a berry bush widely cultivated in Europe for producing juices, jams, jellies, and syrups. In addition to berries, blackcurrant leaves and pomace, as byproducts, have also been shown to have health-promoting effects. Static digestion, simulating oral, gastric, and small intestinal digestion, was applied, and blackcurrant leaves, fruits, and pomace and the polyphenol bioaccessibility were evaluated in terms of recovery index. The results were related to sample type, and the recovery index presented higher values in the case of fruits, indicating this morphological part of blackcurrant as the most bioaccessible. The antioxidant potential of blackcurrant was evaluated using four different methods, with the leaves proving to be a significant and powerful antioxidant compared to fruits and pomace. The counteracting potential of inhibiting the oxidation process was evaluated using in vitro-induced lipid peroxidation and the inhibition potential of superoxide and hydroxyl anions. The antioxidant evaluation and the inhibition of biological and non-biological radicals indicate the leaf extract is the most powerful antioxidant studied. Also, the results proved that not only fruits but also the blackcurrant byproducts (pomace and leaves) are promising sources of bioaccessible antioxidants with potential benefits in animal nutrition.