Subgenomic flavivirus RNAs (sfRNAs) are structured RNAs encoded by flaviviruses that promote viral infection by inhibiting cellular RNA decay machinery. Herein, we analyze sfRNA production and localization using single-molecule RNA fluorescence in situ hybridization (smRNA-FISH) throughout West Nile virus, Zika virus, or dengue virus serotype 2 infection. We observe that sfRNAs are generated during the RNA replication phase of viral infection in the cytosol and accumulate in processing bodies (P-bodies), which contain RNA decay machinery such as XRN1 and Dcp1b. However, upon activation of the host antiviral endoribonuclease, ribonuclease L (RNase L), sfRNAs re-localize to ribonucleoprotein complexes known as RNase L-induced bodies (RLBs). RLB-mediated sequestration of sfRNAs reduces sfRNA association with RNA decay machinery in P-bodies, which coincides with increased viral RNA decay. These findings establish a functional role for RLBs in enhancing the cell-mediated decay of viral RNA by sequestering functional viral RNA decay products.