Vitis vinifera represents an important and renowned source of compounds with significant biological activity. Wines and winery bioproducts, such as grape pomace, skins, and seeds, are rich in bioactive compounds against a wide range of human pathogens, including bacteria, fungi, and viruses. However, little is known about the biological properties of vine leaves. The aim of this study was the evaluation of phenolic composition and antiviral activity of Vitis vinifera leaf extract against two human viruses: the Herpes simplex virus type 1 (HSV-1) and the pandemic and currently widespread severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). About 40 phenolic compounds were identified in the extract by HPLC-MS/MS analysis: most of them were quercetin derivatives, others included derivatives of luteolin, kaempferol, apigenin, isorhamnetin, myricetin, chrysoeriol, biochanin, isookanin, and scutellarein. Leaf extract was able to inhibit both HSV-1 and SARS-CoV-2 replication in the early stages of infection by directly blocking the proteins enriched on the viral surface, at a very low concentration of 10 μg/mL. These results are very promising and highlight how natural extracts could be used in the design of antiviral drugs and the development of future vaccines.