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; 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 three-dimensional organoid cultures. Ten structurally unrelated inhibitors of cyclin-dependent kinases inhibited ZIKV replication. Niclosamide, a category B anthelmintic drug approved by the US Food and Drug Administration, 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.