In response to the current global health emergency posed by the Zika virus (ZIKV) outbreak and its link to microcephaly and other neurological conditions, we performed a drug repurposing screen of ~6,000 compounds that included approved drugs, clinical trial drug candidates and pharmacologically active compounds, and we identified compounds that either inhibit ZIKV infection or suppress infection-induced caspase-3 activity in different neural cells. A pan-caspase inhibitor, Emricasan, inhibited ZIKV-induced increases in caspase-3 activity and protected human cortical neural progenitors in both monolayer and 3-dimensional organoid cultures. Ten structurally unrelated inhibitors of cyclin-dependent kinases inhibited ZIKV replication. Niclosamide, an FDA approved category B anthelmintic drug, also inhibited ZIKV replication. Finally, combination treatments using one compound from each category (neuroprotective and antiviral) further increased protection of human neural progenitors and astrocytes from ZIKV-induced cell death. Our results demonstrate the efficacy of this screening strategy and identify lead compounds for anti-ZIKV drug development.