The coronavirus disease 2019 (COVID-19) has become a serious problem for public health since it was identified in the province of Wuhan (China) and spread around the world producing high mortality rates and economic losses. Nowadays, the WHO recognizes traditional, complementary, and alternative medicine for treating COVID-19 symptoms. Therefore, we investigated the antiviral potential of the hydroalcoholic extract of Uncaria tomentosa stem bark from Peru against SARS-CoV-2 in vitro. The antiviral activity of U. tomentosa against SARS-CoV-2 in vitro was assessed in Vero E6 cells using cytopathic effect (CPE) and plaque reduction assay. After 48 h of treatment, U. tomentosa showed an inhibition of 92.7% of SARS-CoV-2 at 25.0 μg/mL ( p < 0.0001 ) by plaque reduction assay on Vero E6 cells. In addition, U. tomentosa induced a reduction of 98.6% ( p = 0.02 ) and 92.7% ( p = 0.03 ) in the CPE caused by SARS-CoV-2 on Vero E6 cells at 25 μg/mL and 12.5 μg/mL, respectively. The EC50 calculated for the U. tomentosa extract by plaque reduction assay was 6.6 μg/mL (4.89–8.85 μg/mL) for a selectivity index of 4.1. The EC50 calculated for the U. tomentosa extract by TCID50 assay was 2.57 μg/mL (1.05–3.75 μg/mL) for a selectivity index of 10.54. These results showed that U. tomentosa, known as cat's claw, has an antiviral effect against SARS-CoV-2, which was observed as a reduction in the viral titer and CPE after 48 h of treatment on Vero E6 cells. Therefore, we hypothesized that U. tomentosa stem bark could be promising in the development of new therapeutic strategies against SARS-CoV-2.