The most prevalent post-transcriptional mRNA modification, N6-methyladenosine (m6A), plays diverse RNA-regulatory roles, but its genetic control in human tissues remains uncharted. Here we report 129 transcriptome-wide m6A profiles, covering 91 individuals and 4 tissues (brain, lung, muscle and heart) from GTEx/eGTEx. We integrate these with interindividual genetic and expression variation, revealing 8,843 tissue-specific and 469 tissue-shared m6A quantitative trait loci (QTLs), which are modestly enriched in, but mostly orthogonal to, expression QTLs. We integrate m6A QTLs with disease genetics, identifying 184 GWAS-colocalized m6A QTL, including brain m6A QTLs underlying neuroticism, depression, schizophrenia and anxiety; lung m6A QTLs underlying expiratory flow and asthma; and muscle/heart m6A QTLs underlying coronary artery disease. Last, we predict novel m6A regulators that show preferential binding in m6A QTLs, protein interactions with known m6A regulators and expression correlation with the m6A levels of their targets. Our results provide important insights and resources for understanding both cis and trans regulation of epitranscriptomic modifications, their interindividual variation and their roles in human disease.