A copper complex embedded in the structure of a water-soluble naphthalene diimide has been designed to bind and cleave G-quadruplex DNA. We describe the properties of this ligand, including its catalytic activity in the generation of ROS. FRET melting, CD, NMR, gel sequencing, and mass spectrometry experiments highlight a unique and unexpected selectivity in cleaving G-quadruplex sequences. This selectivity relies both on the binding affinity and structural features of the targeted G-quadruplexes.