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 N6-methyladenosine (m6A) in their 5′ UTR can be translated in a cap-independent manner. A single 5′ UTR m6A 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 m6A. Additionally, increased m6A 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 m6A, resulting in increased numbers of mRNAs with 5′ UTR m6A. These data show that 5′ UTR m6A bypasses 5′ cap-binding proteins to promote translation under stresses. Display omitted •m6A residues within the 5′ UTR promote cap-independent translation•Translation of cellular mRNAs is increased by the presence of m6A within the 5′ UTR•Heat shock induces Hsp70 translation in an m6A-dependent manner•Diverse cellular stresses increase 5′ UTR adenosine methylation N6-methyladenosine (m6A) residues within the 5′ UTR of mRNAs promote translation initiation through a mechanism that does not require the 5′ cap or cap-binding proteins. Diverse cellular stresses selectively increase the levels of m6A within 5′ UTRs, suggesting that 5′ UTR m6A is important for mediating stress-induced translational responses.