Therapies to prevent maternal Zika virus (ZIKV) infection and its subsequent fetal developmental complications are urgently required. We isolated three potent ZIKV-neutralizing monoclonal antibodies (nmAbs) from the plasmablasts of a ZIKV-infected patient—SMZAb1, SMZAb2, and SMZAb5—directed against two different domains of the virus. We engineered these nmAbs with Fc LALA mutations that abrogate Fcγ receptor binding, thus eliminating potential therapy-mediated antibody-dependent enhancement. We administered a cocktail of these three nmAbs to nonhuman primates 1 day before challenge with ZIKV and demonstrated that the nmAbs completely prevented viremia in serum after challenge. Given that numerous antibodies have exceptional safety profiles in humans, the cocktail described here could be rapidly developed to protect uninfected pregnant women and their fetuses.