The use of click chemistry for quantum dot (QD) functionalization could be very promising for the development of bioconjugates dedicated to in vivo applications. Alkyne-azide ligation usually requires copper(I) catalysis. The luminescence response of CdSeTe/ZnS nanoparticles coated with polyethylene glycol (PEG) is studied in the presence of copper cations, and compared to that of InP/ZnS QDs coated with mercaptoundecanoic acid (MUA). The quenching mechanisms appear different. Luminescence quenching occurs without any wavelength shift in the absorption and emission spectra for the CdSeTe/ZnS/PEG nanocrystals. In this case, the presence of copper in the ZnS shell is evidenced by energy-filtered transmission electron microscopy (EF-TEM). By contrast, in the case of InP/ZnS/MUA nanocrystals, a redshift of the excitation and emission spectra, accompanied by an increase in absorbance and a decrease in photoluminescence, is observed. For CdSeTe/ZnS/PEG nanocrystals, PL quenching is enhanced for QDs with 1) smaller inorganic-core diameter, 2) thinner PEG shell, and 3) hydroxyl terminal groups. Whereas copper-induced PL quenching can be interesting for the design of sensitive cation sensors, copper-free click reactions should be used for the efficient functionalization of nanocrystals dedicated to bioapplications, in order to achieve highly luminescent QD bioconjugates.