The discarding of agri-food by-products is a stringent problem due to their high environmental impact. Recovery strategies can lead to a reduction of waste and result in new applications. Agri-food waste represents a source of bioactive molecules, which could promote health benefits. The primary goal of this research has been the assessment of the antioxidant activity of milk permeate, a dairy farm by-product, and the isolation and identification of peptide fractions endowed with antioxidant activity. The chromatographic extraction of the peptide fractions was carried out, and the peptides were identified by mass spectrometry. The fractions showed radical scavenging activity in vitro. Moreover, the results in the Caco-2 cell model demonstrated that the peptide fractions were able to protect from oxidative stress by stimulating the Keap1/Nrf2 antioxidant signaling pathway, increasing the transcription of antioxidant enzymes. In addition, the bioactive peptides can affect cellular metabolism, increasing mitochondrial respiration. The action of the peptide fractions was also assessed in vivo on a zebrafish model and resulted in the protection of the whole organism from the adverse effects of acute cold stress, highlighting their strong capability to protect from an oxidative insult. Altogether, the results unveil novel recovery strategies for food by-products as sources of antioxidant bioactive peptides that might be utilized for the development of functional foods.