The establishment of a sylvatic reservoir of Zika virus (ZIKV) in the Americas is dependent on the susceptibility of primates of sufficient population density, the duration and magnitude of viremia, and their exposure to the human mosquito-borne transmission cycle. To assess the susceptibility of squirrel (Saimiri sp.) and owl monkeys (Aotus sp.) to infection, we inoculated four animals of each species with ZIKV from the current epidemic. Viremia in the absence of detectible disease was observed in both species and seroconversion occurred by day 28. ZIKV was detected in the spleen of three owl monkeys: one at 7 days postinoculation (dpi) and two at 14 dpi. This study confirms the susceptibility to ZIKV infection of two Neotropical primate species that live in close proximity to humans in South America, suggesting that they could support a widespread sylvatic ZIKV cycle there. Collectively, establishment of a ZIKV sylvatic transmission cycle in South America would imperil eradication efforts and could provide a mechanism for continued exposure of humans to ZIKV infection and disease.