In the presence of physiological monovalent cations, thousands of RNA G-rich sequences can form parallel G-quadruplexes (G4s) unless RNA-binding proteins inhibit, destabilize, or resolve the formation of such secondary RNA structures. Here, we have used a disease-relevant model system to investigate the biophysical properties of the RNA-binding protein HNRNPH1’s interaction with G-rich sequences. We demonstrate the importance of two EWSR1-exon 8 G-rich regions in mediating the exclusion of this exon from the oncogenic EWS-FLI1 transcripts expressed in a subset of Ewing sarcomas, using complementary analysis of tumor data, long-read sequencing, and minigene studies. We determined that HNRNPH1 binds the EWSR1-exon 8 G-rich sequences with low nM affinities irrespective of whether in a non-G4 or G4 state but exhibits different kinetics depending on RNA structure. Specifically, HNRNPH1 associates and dissociates from G4-folded RNA faster than the identical sequences in a non-G4 state. Importantly, we demonstrate using gel shift and spectroscopic assays that HNRNPH1, particularly the qRRM1-qRRM2 domains, destabilizes the G4s formed by the EWSR1-exon 8 G-rich sequences in a non-catalytic fashion. Our results indicate that HNRNPH1’s binding of G-rich sequences favors the accumulation of RNA in a non-G4 state and that this contributes to its regulation of RNA processing.