Coronavirus disease 2019 (COVID‐19), caused by severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2), was declared a pandemic by the World Health Organization in March 2020. Since then, viral spread from humans to animals has occurred worldwide. Nonhuman primates (NHPs) have been found to be susceptible to reverse‐zoonosis transmission of SARS‐CoV‐2, but initial research suggested that platyrrhine primates are less susceptible than catarrhine primates. Here we report the natural SARS‐CoV‐2 infection of a common woolly monkey (Lagothrix lagothricha) from a wildlife rehabilitation center in Ecuador. The course of the disease, the eventual death of the specimen, and the pathological findings are described. Our results show the susceptibility of a new platyrrhine species to SARS‐CoV‐2 and provide evidence for the first time of a COVID‐19‐associated death in a naturally infected NHP. The putative route of transmission from humans, and implications for captive NHPs management, are also discussed. Given that common woolly monkeys are at risk of extinction in Ecuador, further understanding of the potential threat of SARS‐CoV‐2 to their health should be a conservation priority. A One Health approach is the best way to protect NHPs from a new virus in the same way that we would protect the human population.