Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly become a global health pandemic. Among the viral proteins, RNA-dependent RNA polymerase (RdRp) is responsible for viral genome replication and has emerged as one of the most promising targets for pharmacological intervention against SARS-CoV-2. To this end, we experimentally tested luteolin and quercetin for their ability to inhibit the RdRp enzyme. These two compounds are ancestors of flavonoid natural compounds known for a variety of basal pharmacological activities. Luteolin and quercetin returned a single-digit IC50 of 4.6 µM and 6.9 µM, respectively. Then, through dynamic docking simulations, we identified possible binding modes of these compounds to a recently published cryo-EM structure of RdRp. Collectively, these data indicate that these two compounds are a valid starting point for further optimization and development of a new class of RdRp inhibitors to treat SARS-CoV-2 and potentially other viral infections.