As a developmental toxicant, Zika virus (ZIKV) attacks both the growing nervous system, causing congenital Zika syndrome, and the placenta, resulting in pathological changes and associated adverse fetal outcomes. There are no vaccines, antibodies, or other treatments for ZIKV, despite the potential for its re-emergence. Multiple studies have highlighted the risk of antibodies for enhancing ZIKV infection, including during pregnancy, but the mechanisms for such effects are not fully understood. We have focused on the ability of the neonatal Fc receptor (FcRn) to interact with ZIKV in the presence and absence of relevant antibodies. We found that ZIKV replication was higher in Marvin Darby Canine Kidney (MDCK) cells that overexpress FcRn compared to those that do not, and knocking down FcRn decreased ZIKV RNA production. In the placenta trophoblast BeWo cell line, ZIKV infection itself downregulated FcRn at the mRNA and protein levels. Addition of anti-ZIKV antibodies to MDCK/FcRn cells resulted in non-monotonous neutralization curves with neutralization attenuation and even enhancement of infection at higher concentrations. Non-monotonous neutralization was also seen in BeWo cells at intermediate antibody concentrations. Our studies highlight the underappreciated role FcRn plays in ZIKV infection and may have implications for anti-ZIKV prophylaxis and therapy in pregnant women.