The Oropouche virus is an orthobunyavirus responsible for causing Oropouche fever, a disease that primarily affects thousands of people in South and Central America. Currently, no specific antiviral treatments or vaccines are available against this virus, highlighting the urgent need for safe, affordable, and effective therapies. Natural products serve as an important source of bioactive compounds, and there is growing interest in identifying natural bioactive molecules that could be used for treating viral diseases. Quercetin hydrate is a compound classified as a flavonoid, which has garnered scientific attention due to its potential health benefits and its presence in various plant-based foods. In this study, we aim to evaluate the in vitro antiviral activity of quercetin hydrate against the Oropouche virus (OROV). Furthermore, we intend to explore its mode of action through in silico approaches. The cytotoxicity and antiviral activity of the compound were assessed using Vero cells. In addition, in silico studies were also performed through molecular docking, molecular dynamics simulations, Molecular Mechanics Poisson–Boltzmann surface area (MM/PBSA), and quantum-mechanical analysis in order to evaluate the interaction with the Gc protein of OROV. The assay revealed that the compound was highly active against the virus, inhibiting OROV with an EC50 value of 53.5 ± 26.5 µM under post-infection treatment conditions. The present study demonstrates that the compound is a promising antiviral agent; however, the mechanisms of action proposed in this study need to be experimentally verified by future assays.