The copper sequestering ability of melatonin and its metabolites cyclic 3-hydroxymelatonin (3OHM), N1-acetyl-N2-formyl-5-methoxykynuramine (AFMK), and N1-acetyl-5-methoxykynuramine (AMK) was investigated within the frame of the Density Functional Theory. It was demonstrated that these compounds are capable of chelating copper ions, yielding stable complexes. The most likely chelation sites were identified. Two different mechanisms were modeled, the direct-chelation mechanism (DCM) and the coupled-deprotonation-chelation mechanism (CDCM). It is proposed that, under physiological conditions, CDCM would be the main chelation route for Cu(II). It was found that melatonin and its metabolites fully inhibited the oxidative stress induced by Cu(II)-ascorbate mixtures, via Cu(II) chelation. In the same way, melatonin, AFMK, and 3OHM also prevented the first step of the Haber–Weiss reaction, consequently turning off the ·OH production via the Fenton reaction. Therefore, it is proposed that, in addition to the previously reported free radical scavenging cascade, melatonin is also involved in a concurrent ‘chelating cascade’, thereby contributing to a reduction in oxidative stress. 3OHM was identified as the most efficient of the studied compounds for that purpose, supporting the important role of this metabolite in the beneficial effects of melatonin against oxidative stress.