N(6)-methyladenosine (m6A) is the most abundant modified base in eukaryotic mRNA and has been linked to diverse effects on mRNA fate. Current mapping approaches localize m6A residues to transcript regions 100-200 nt long but cannot identify precise m6A positions on a transcriptome-wide level. Here we developed m6A individual-nucleotide-resolution cross-linking and immunoprecipitation (miCLIP) and used it to demonstrate that antibodies to m6A can induce specific mutational signatures at m6A residues after ultraviolet light-induced antibody-RNA cross-linking and reverse transcription. We found that these antibodies similarly induced mutational signatures at N(6),2'-O-dimethyladenosine (m6Am), a modification found at the first nucleotide of certain mRNAs. Using these signatures, we mapped m6A and m6Am at single-nucleotide resolution in human and mouse mRNA and identified small nucleolar RNAs (snoRNAs) as a new class of m6A-containing non-coding RNAs (ncRNAs).