Protein translation typically begins with the recruitment of the 43S ribosomal complex to the 5' cap of mRNAs by a cap-binding complex. However, some transcripts are translated in a cap-independent manner through poorly understood mechanisms. Here, we show that mRNAs containing N(6)-methyladenosine (m(6)A) in their 5' UTR can be translated in a cap-independent manner. A single 5' UTR m(6)A directly binds eukaryotic initiation factor 3 (eIF3), which is sufficient to recruit the 43S complex to initiate translation in the absence of the cap-binding factor eIF4E. Inhibition of adenosine methylation selectively reduces translation of mRNAs containing 5'UTR m(6)A. Additionally, increased m(6)A levels in the Hsp70 mRNA regulate its cap-independent translation following heat shock. Notably, we find that diverse cellular stresses induce a transcriptome-wide redistribution of m(6)A, resulting in increased numbers of mRNAs with 5' UTR m(6)A. These data show that 5' UTR m(6)A bypasses 5' cap-binding proteins to promote translation under stresses.