Zika virus (ZIKV) is a major public health concern due to its overwhelming spread into the Americas. Currently, there are neither licensed vaccines nor antiviral therapies available for the treatment of ZIKV. We aimed to identify and rationally optimize effective therapeutic regimens for ZIKV by evaluating the antiviral potentials of the approved broad-spectrum antiviral agents favipiravir (FAV), interferon alpha (IFN), and ribavirin (RBV) as single agents and in combinations. For these studies, Vero cells were infected with ZIKV in the presence of increasing concentrations of FAV, IFN, or/and RBV for 4 days. Supernatants were harvested daily, and the viral burden was quantified by a plaque assay on Vero cells. The time course of the viral burden during treatment in vitro was characterized by a novel translational, mechanism-based model, which was subsequently used to rationally optimize combination dosage regimens. The combination regimen of FAV plus IFN provided the greatest extent of viral inhibition without cytotoxicity, reducing the viral burden by 4.4 log 10 PFU/ml at concentrations of 250 M FAV and 100 IU/ml IFN. Importantly, these concentrations are achievable in humans. The translational, mechanism-based model yielded unbiased and reasonably precise curve fits. Simulations with the model predicted that clinically relevant regimens of FAV plus IFN would markedly reduce viral burdens in humans, resulting in at least a 10,000-fold reduction in the amount of the virus during the first 4 days of treatment. These findings highlight the substantial promise of rationally optimized combination dosage regimens of FAV plus IFN, which should be further investigated to combat ZIKV.