Strategies to treat Zika virus (ZIKV) infection in dengue virus (DENV)-endemic areas are urgently needed. Here we show that a DENV-specific antibody against the E-dimer epitope (EDE) potently cross-neutralizes ZIKV and provides robust therapeutic efficacy as well as prophylactic efficacy against ZIKV in rhesus monkeys. Viral escape was not detected, suggesting a relatively high bar to escape. These data demonstrate the potential for antibody-based therapy and prevention of ZIKV.