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.