Identification of a suitable nonhuman primate (NHP) model of COVID-19 remains challenging. Here, we characterized severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in three NHP species: Old World monkeys Macaca mulatta (M. mulatta) and Macaca fascicularis (M. fascicularis) and New World monkey Callithrix jacchus (C. jacchus). Infected M. mulatta and M. fascicularis showed abnormal chest radiographs, an increased body temperature and a decreased body weight. Viral genomes were detected in swab and blood samples from all animals. Viral load was detected in the pulmonary tissues of M. mulatta and M. fascicularis but not C. jacchus. Furthermore, among the three animal species, M. mulatta showed the strongest response to SARS-CoV-2, including increased inflammatory cytokine expression and pathological changes in the pulmonary tissues. Collectively, these data revealed the different susceptibilities of Old World and New World monkeys to SARS-CoV-2 and identified M. mulatta as the most suitable for modeling COVID-19.