The RNA modification N6-methyladenosine (m6A) modulates mRNA fate and thus affects many biological processes. We analyzed m6A across the transcriptome following infection by dengue virus (DENV), Zika virus (ZIKV), West Nile virus (WNV), and hepatitis C virus (HCV). We found that infection by these viruses in the Flaviviridae family alters m6A modification of specific cellular transcripts, including RIOK3 and CIRBP. During viral infection, the addition of m6A to RIOK3 promotes its translation, while loss of m6A in CIRBP promotes alternative splicing. Importantly, viral activation of innate immune sensing or the endoplasmic reticulum (ER) stress response contributes to the changes in m6A in RIOK3 or CIRBP, respectively. Further, several transcripts with infection-altered m6A profiles, including RIOK3 and CIRBP, encode proteins that influence DENV, ZIKV, and HCV infection. Overall, this work reveals that cellular signaling pathways activated during viral infection lead to alterations in m6A modification of host mRNAs to regulate infection.