Zika virus (ZIKV) can infect developing fetuses in utero and cause severe congenital defects independent of route of maternal infection. Infected men can shed ZIKV RNA in semen for over six months. Whether prolonged viral RNA shedding in semen indicates a persistent infection in the male reproductive tract is unknown. We hypothesized that if ZIKV establishes a persistent infection in the male reproductive tract (MRT), then immunosuppressant treatment should stimulate ZIKV replication and seminal shedding. Male mice were infected with ZIKV and immunosuppressed when they shed viral RNA but not infectious virus in ejaculates. Following immunosuppression, we did not detect infectious virus in ejaculates. However, we did detect ZIKV positive and negative sense RNA in the epididymal lumens of mice treated with cyclophosphamide, suggesting that ZIKV persists in the epididymis. This study provides insight into the mechanisms behind ZIKV sexual transmission, which may inform public health decisions regarding ZIKV risks.