Zika virus (ZIKV), an emerging flavivirus, has recently spread explosively through the Western hemisphere. In addition to symptoms including fever, rash, arthralgia, and conjunctivitis, ZIKV infection of pregnant women can cause microcephaly and other developmental abnormalities in the fetus. We report herein the results of ZIKV infection of adult rhesus macaques. Following subcutaneous infection, animals developed transient plasma viremia and viruria from 1–7 days post infection (dpi) that was accompanied by the development of a rash, fever and conjunctivitis. Animals produced a robust adaptive immune response to ZIKV, although systemic cytokine response was minimal. At 7 dpi, virus was detected in peripheral nervous tissue, multiple lymphoid tissues, joints, and the uterus of the necropsied animals. Notably, viral RNA persisted in neuronal, lymphoid and joint/muscle tissues and the male and female reproductive tissues through 28 to 35 dpi. The tropism and persistence of ZIKV in the peripheral nerves and reproductive tract may provide a mechanism of subsequent neuropathogenesis and sexual transmission.