Antioxidant peptides positively regulate oxidative stress in the human body as well as delay, retard or prevent protein and lipid oxidation in food products. Spanish dry-cured ham has been reported as a good source of bioactive peptides, being SNAAC the most active antioxidant peptide identified to date. In this work, the stability of this peptide against in vitro digestion, heat treatments and different salt concentrations was evaluated using three methods for measuring antioxidant activity: β-carotene bleaching assay, ABTS radical scavenging capacity and ORAC assay. The results evidenced a marked decrease in the antioxidant activity of SNAAC after gastrointestinal digestion, and the MALDI-ToF MS analysis revealed the degradation of the peptide after the process, the generation of the fragment SNAA and the presence of a peptide dimer throughout the in vitro digestion. On the other hand, the peptide SNAAC showed good heat stability after exposure to different temperatures (50 °C, 72 °C, and 90 °C), but its antioxidant activity evaluated by ORAC assay decreased substantially when exposed to 100 °C as compared with the control at 37 °C. SNAAC remained stable in the presence of salt at concentrations ranging from 0 to 8% NaCl as well as it was able to inhibit about 40% of lipid oxidation in an emulsion system. These results reported the stability of the antioxidant peptide SNAAC to several conditions used in meat industry for the processing of dry-cured hams and ham-derived products and its effectiveness to partially prevent the lipid oxidation in these products. However, some strategies would be needed in order to increase the stability of the peptide during gastrointestinal digestion and thus improve its bioavailability for its use as functional food ingredient.