From January 2020, COVID-19 is spreading around the world producing serious respiratory symptoms in infected patients that in some cases can be complicated by the severe acute respiratory syndrome, sepsis and septic shock, multiorgan failure, including acute kidney injury and cardiac injury. Cost and time efficient approaches to reduce the burthen of the disease are needed. To find potential COVID-19 treatments among the whole arsenal of existing drugs, we combined system biology and artificial intelligence-based approaches. The drug combination of pirfenidone and melatonin has been identified as a candidate treatment that may contribute to reduce the virus infection. Starting from different drug targets the effect of the drugs converges on human proteins with a known role in SARS-CoV-2 infection cycle. Simultaneously, GUILDify v2.0 web server has been used as an alternative method to corroborate the effect of pirfenidone and melatonin against the infection of SARS-CoV-2. We have also predicted a potential therapeutic effect of the drug combination over the respiratory associated pathology, thus tackling at the same time two important issues in COVID-19. These evidences, together with the fact that from a medical point of view both drugs are considered safe and can be combined with the current standard of care treatments for COVID-19 makes this combination very attractive for treating patients at stage II, non-severe symptomatic patients with the presence of virus and those patients who are at risk of developing severe pulmonary complications.