Infection of pregnant women with Zika virus (ZIKV) can cause congenital malformations including microcephaly, which has focused global attention on this emerging pathogen. In addition to transmission by mosquitoes, ZIKV can be detected in the seminal fluid of affected males for extended periods of time and transmitted sexually. Here, using a mouse-adapted African ZIKV strain (Dakar 41519), we evaluated the consequences of infection in the male reproductive tract of mice. We observed persistence of ZIKV, but not the closely related dengue virus (DENV), in the testis and epididymis of male mice, and this was associated with tissue injury that caused diminished testosterone and inhibin B levels and oligospermia. ZIKV preferentially infected spermatogonia, primary spermatocytes and Sertoli cells in the testis, resulting in cell death and destruction of the seminiferous tubules. Less damage was caused by a contemporary Asian ZIKV strain (H/PF/2013), in part because this virus replicates less efficiently in mice. The extent to which these observations in mice translate to humans remains unclear, but longitudinal studies of sperm function and viability in ZIKV-infected humans seem warranted.