Animal models of Zika virus (ZIKV) are needed to better understand tropism and pathogenesis and to test candidate vaccines and therapies to curtail the pandemic. Humans and rhesus macaques possess similar fetal development and placental biology that is not shared between humans and rodents. We inoculated 2 non-pregnant rhesus macaques with a 2015 Brazilian ZIKV strain. Consistent with most human infections, the animals experienced no clinical disease but developed short-lived plasma viremias that cleared as neutralizing antibody developed. In 1 animal, viral RNA (vRNA) could be detected longer in whole blood than in plasma. Despite no major histopathologic changes, many adult tissues contained vRNA 14 days post-infection with highest levels in hemolymphatic tissues. These observations warrant further studies to investigate ZIKV persistence and its potential clinical implications for transmission via blood products or tissue and organ transplants.