In the present work, and for the first time, three whey protein-derived peptides (IAEK, IPAVF, MHI), endowed with ACE inhibitory activity, were examined for their antiviral activity against the SARS-CoV-2 3C-like protease (3CL(pro)) and Human Rhinovirus 3C protease (3C(pro)) by employing molecular docking. Computational studies showed reliable binding poses within 3CL(pro) for the three investigated small peptides, considering docking scores as well as the binding free energy values. Validation by in vitro experiments confirmed these results. In particular, IPAVF exhibited the highest inhibitory activity by returning an IC50 equal to 1.21 muM; it was followed by IAEK, which registered an IC50 of 154.40 muM, whereas MHI was less active with an IC50 equal to 2700.62 muM. On the other hand, none of the assayed peptides registered inhibitory activity against 3C(pro). Based on these results, the herein presented small peptides are introduced as promising molecules to be exploited in the development of "target-specific antiviral" agents against SARS-CoV-2.