Coronavirus disease 2019 (COVID-19), a viral infectious respiratory disease, is caused by highly contagious severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and is responsible for the ongoing COVID-19 pandemic. Since very few drugs are known to be effective against SARS-CoV-2, there is a general need for new therapeutics, including plant-based drugs, for the prophylaxis and treatment of infections. In the current study, the activity of a 70% ethanolic(aq) extract of the rhizome bark of Japanese knotweed, an invasive alien plant species, was tested for the first time against the wild-type SARS-CoV-2 virus using a specific and robust virus neutralization test (VNT) on Vero-E6 cells, which best mimics the mechanism of real virus–host interaction. A statistically significant antiviral effect against SARS-CoV-2 (p-value < 0.05) was observed for the 50.8 µg mL−1 extract solution in cell medium. A suitable extract preparation was described to avoid loss of polyphenols throughout filtration of the extract, which was dissolved in cell medium containing fetal bovine serum (FBS). The significance of the differences between the sums of the test and control groups in the incidence of cytopathic effects (CPE) was determined using the one-way ANOVA test. A dose–response relationship was observed, with the cytotoxic effect occurring at higher concentrations of the extract (≥101.6 µg mL−1). The obtained results suggest possible use of this plant material for the production of various products (e.g., packaging, hygiene products, biodisinfectants, etc.) that would be useful against the spread of and for self-protection against COVID-19.