The emergence of the novel coronavirus SARS-CoV-2, which in humans is highly infectious and leads to the potentially fatal disease COVID-19, has caused hundreds of thousands of deaths and huge global disruption. The viral infection may also represent an existential threat to our closest living relatives, the nonhuman primates, many of which are endangered and often reduced to small populations. The virus engages the host cell receptor, angiotensin-converting enzyme-2 (ACE2), through the receptor binding domain (RBD) on the spike protein. The contact surface of ACE2 displays amino acid residues that are critical for virus recognition, and variations at these critical residues are likely to modulate infection susceptibility across species. While infection studies are emerging and have shown that some primates, such as rhesus macaques and vervet monkeys, develop COVID-19-like symptoms when exposed to the virus, the susceptibility of many other nonhuman primates is unknown. Here, we show that all apes, including chimpanzees, bonobos, gorillas, and orangutans, and all African and Asian monkeys (catarrhines), exhibit the same set of twelve key amino acid residues as human ACE2. Monkeys in the Americas, and some tarsiers, lemurs and lorisoids, differ at significant contact residues, and protein modeling predicts that these differences should greatly reduce the binding affinity of the ACE2 for the virus, hence moderating their susceptibility for infection. Other lemurs are predicted to be closer to catarrhines in their susceptibility. Our study suggests that apes and African and Asian monkeys, as well as some lemurs are all likely to be highly susceptible to SARS-CoV-2, representing a critical threat to their survival. Urgent actions have been undertaken to limit the exposure of Great Apes to humans, and similar efforts may be necessary for many other primate species. ### Competing Interest Statement The authors have declared no competing interest.