Although Zika virus (ZIKV) is primarily transmitted to humans by the Aedes aegypti mosquito, human-to-human transmission has also been observed from males-to-females as well as mother-to-offspring. In the current study, we studied both sexual transmission (STx) and vertical transmission (VTx) of ZIKV using anti-IFNAR1-treatment of Rag1 -/- (AIR) mice. These mice have suppressed type I IFN responses and lack adaptive immune responses, leading to a prolonged infection prior to clinical disease. STx of ZIKV from infected AIR males to naive Ifnar1 -/- females was observed with greater than 50% incidence, with infection observed in the vaginal tract at early time points. In the case of a resulting pregnancy, virus was also found in the uterus and placental tissue. In additional studies, VTx of virus was observed in AIR female mice. Specifically, peripheral ZIKV infection of pregnant AIR females resulted in detectable virus in brain and/or lymph nodes of fetuses and/or pups. VTx of ZIKV was stochastic, in that not all fetuses/pups within the same dam had detectable virus and infection was not associated with breakdown of maternal/fetal placental barrier. This provides a new model to study the barriers to STx and VTx of ZIKV and the immune responses essential to preventing transmission.