Zika virus has recently emerged as an important human pathogen that has spread to more than 60 countries. Infection of a pregnant woman with Zika virus can cause severe brain malformations in the child such as microcephaly and other birth defects. Despite the medical importance of Zika virus infection, the mechanism of viral replication, a process commonly targeted by antiviral therapeutics, is not well understood. Stem-loop A (SLA), located in the 5′ untranslated region of the viral genome, acts as a promotor for viral replication and thus is critical for recognition of the viral genome by the viral polymerase NS5. However, how NS5 engages SLA is not clear. We have quantitatively examined the intrinsic affinities between Zika virus SLA and NS5, and identified the SLA-binding site on NS5. Amino acid substitutions in the thumb subdomain of the RNA-dependent RNA polymerase (RdRp) and the methyltransferase (MTase) domain reduced SLA-binding affinity, indicating that they each are part of the SLA-binding site. Furthermore, stopped-flow kinetic analysis of Zika NS5-, RdRp- and MTase-SLA interactions identified distinct intermediates during NS5 and SLA complex formation. These data suggest a model for SLA recognition and the initiation of flaviviral replication by NS5.