The rapid spread of Zika virus (ZIKV) in recent years has highlighted the severe diseases associated with ZIKV infection, such as Guillain-Barré syndrome in adults and microcephaly in newborns; yet no vaccines or antivirals currently exist to prevent or treat ZIKV infection. We and others have previously identified N-(4-hydroxyphenyl) retinamide (fenretinide or 4-HPR) as an antiviral compound that inhibits dengue virus 2 (DV2) and other flaviviruses by limiting the steady-state accumulation of viral RNA. Here we show that 4-HPR potently inhibits ZIKV in mammalian cell culture and significantly reduces both serum viremia and brain viral burden in a murine model of ZIKV infection. Consistent with previous observations with dengue virus, this antiviral activity is associated with a significant reduction in the steady-state abundance of viral genomic RNA. We show this reduction is due to a major decrease in the rate of viral RNA synthesis, though not via direct inhibition of the activity of the viral replicase. These results establish 4-HPR's mode of action against DV and ZIKV and, taken with previous clinical trials that established 4-HPR's safety and tolerability, illustrate the potential utility of 4-HPR as an agent for treatment of ZIKV infection.