Zika virus (ZIKV), one of the flaviviruses, has attracted worldwide attention since its large epidemics around Brazil. Association of ZIKV infection with microcephaly and neurological problems such as Guillain–Barré syndrome has prompted intensive pathological investigations. However, there is still a long way to go on the discovery of effective anti-ZIKV therapeutics. In this study, an in silico screening of the National Cancer Institute (NCI) diversity set based on ZIKV NS3 helicase was performed using a molecular docking approach. Selected compounds with drug-like properties were subjected to cell-based antiviral assays resulting in the identification of two novel lead compounds (named Compounds 1 and 2). They inhibited ZIKV infection with IC50 values at the micro-molar level (8.5 μM and 15.2 μM, respectively). Binding mode analysis, absolute binding free energy calculation, and structure–activity relationship studies of these two compounds revealed their possible interactions with ZIKV NS3 helicase, suggesting a mechanistic basis for further optimization. These two novel small molecules may represent new leads for the development of inhibitory drugs against ZIKV.