Reversible post-transcriptional modifications on messenger RNA emerge as prevalent phenomena in RNA metabolism. The most abundant among them is N6-methyladenosine (m6A) which is pivotal for RNA metabolism and function; its role in stress response remains elusive. We have discovered that in response to oxidative stress, transcripts are additionally m6A modified in their 5' vicinity. Distinct from that of the translationally active mRNAs, this methylation pattern provides a selective mechanism for triaging mRNAs from the translatable pool to stress-induced stress granules. These stress-induced newly methylated sites are selectively recognized by the YTH domain family 3 (YTHDF3) "reader" protein, thereby revealing a new role for YTHDF3 in shaping the selectivity of stress response. Our findings describe a previously unappreciated function for RNA m6A modification in oxidative-stress response and expand the breadth of physiological roles of m6A.