Zika virus (ZIKV) has recently surged in human populations, causing an increase in congenital and Guillain-Barré syndromes. While sexual transmission and presence of ZIKV in urine, semen, vaginal secretions, and saliva have been established, the origin of persistent virus shedding into biological secretions is not clear. Using a primary adult murine neuronal culture model, we have determined that ZIKV persistently and productively infects sensory neurons of the trigeminal and dorsal root ganglia, which innervate glands and mucosa of the face and the genitourinary tract, respectively, without apparent injury. Autonomic neurons that innervate these regions are not permissive for infection. However, productive ZIKV infection of satellite glial cells that surround and support sensory and autonomic neurons in peripheral ganglia results in their destruction. Persistent infection of sensory neurons, without affecting their viability, provides a potential reservoir for viral shedding in biological secretions for extended periods of time after infection. Furthermore, viral destruction of satellite glial cells may contribute to the development of Guillain-Barré Syndrome via an alternative mechanism to the established autoimmune response.