Epitranscriptomic RNA modifications can serve as recognition elements for the recruitment of effector proteins (i.e., "readers") to modified transcripts. While these interactions play an important role in mRNA regulation, there is a major gap in our understanding of the sequence determinants critical for the binding of readers to modified sequence motifs. Here, we develop a high-throughput platform, relying upon selection with a site-specifically modified random sequence RNA library and next-generation sequencing, to profile the binding specificity of RNA modification reader proteins. We apply our approach to interrogate the effect of sequence context on the interactions of YTH-domain proteins with N-methyladenosine (mA)-modified RNA. We find that while the binding preferences of YTHDC1 strongly overlap with the well-characterized DR(mA)CH motif, the related YTH-domain proteins YTHDF1 and YTHDF2 can bind tightly to noncanonical mA-containing sequences. Our results reveal the principles underlying substrate selection by mA reader proteins and provide a powerful approach for investigating protein-modified RNA interactions in an unbiased manner.