One of the most recent advances in the analysis of viral RNA–cellular protein interactions is the Comprehensive Identification of RNA-binding Proteins by Mass Spectrometry (ChIRP-MS). Here, we used ChIRP-MS in mock-infected and Zika-infected wild-type cells and cells knockout for the zinc finger CCCH-type antiviral protein 1 (ZAP). We characterized “ZAP-independent” and “ZAP-dependent” cellular protein interactomes associated with flavivirus RNA and found that ZAP affects cellular proteins associated with Zika virus RNA. The ZAP-dependent interactome identified with ChIRP-MS provides potential ZAP co-factors for antiviral activity against Zika virus and possibly other viruses. Identifying the full spectrum of ZAP co-factors and mechanisms of how they act will be critical to understanding the ZAP antiviral system and may contribute to the development of antivirals.