G-quadruplex (G4) structures formed by the guanine-rich DNA regions exhibit several distinctive optical properties, including UV absorption and circular dichroism spectra. Some G4 DNA possess intrinsic UV fluorescence whose origin is not completely clear to date. In this work, we study the effect of TMPyP4 and Methylene Blue on the intrinsic fluorescence of the dimeric G4 DNA structure formed by two d(G3T)4 sequences. We demonstrate that binding of the ligands results in quenching of the intrinsic fluorescence, although the conformation of the G4 DNA and its dimeric structure remain preserved. The binding sites of the ligands were suggested by the photoinduced oxidation of guanines and analysis of binding isoterms. We discuss how DNA-ligand complexes can affect the intrinsic fluorescence of G4 DNA.