Insect-borne flaviviruses produce a 300-500-base long noncoding RNA, termed subgenomic flavivirus RNA (sfRNA), by stalling the cellular 5'-3'-exoribonuclease 1 (XRN1) via structures located in their 3' UTRs. In this study, we demonstrate that sfRNA production by Zika virus represses XRN1 analogous to what we have previously shown for other flaviviruses. Using protein-RNA reconstitution and a stringent RNA pulldown assay with human choriocarcinoma (JAR) cells, we demonstrate that the sfRNAs from both dengue type 2 and Zika viruses interact with a common set of 21 RNA-binding proteins that contribute to the regulation of post-transcriptional processes in the cell, including splicing, RNA stability, and translation. We found that four of these sfRNA-interacting host proteins, DEAD-box helicase 6 (DDX6) and enhancer of mRNA decapping 3 (EDC3) (two RNA decay factors), phosphorylated adaptor for RNA export (a regulator of the biogenesis of the splicing machinery), and apolipoprotein B mRNA-editing enzyme catalytic subunit 3C (APOBEC3C, a nucleic acid-editing deaminase), inherently restrict Zika virus infection. Furthermore, we demonstrate that the regulations of cellular mRNA decay and RNA splicing are compromised by Zika virus infection as well as by sfRNA alone. Collectively, these results reveal the large extent to which Zika virus-derived sfRNAs interact with cellular RNA-binding proteins and highlight the potential for widespread dysregulation of post-transcriptional control that likely limits the effective response of these cells to viral infection.