Zinc therapy is normally utilized for treatment of Wilson disease (WD), an inherited condition that is characterized by increased levels of non-ceruloplasmin bound (‘free’) copper in serum and urine. A subset of patients with Alzheimer’s disease (AD) or its prodromal form, known as Mild Cognitive Impairment (MCI), fail to maintain a normal copper metabolic balance and exhibit higher than normal values of non-ceruloplasmin copper. Zinc’s action mechanism involves the induction of intestinal cell metallothionein, which blocks copper absorption from the intestinal tract, thus restoring physiological levels of non-ceruloplasmin copper in the body. On this basis, it is employed in WD. Zinc therapy has shown potential beneficial effects in preliminary AD clinical trials, even though the studies have missed their primary endpoints, since they have study design and other important weaknesses. Nevertheless, in the studied AD patients, zinc effectively decreased non-ceruloplasmin copper levels and showed potential for improved cognitive performances with no major side effects. This review discusses zinc therapy safety and the potential therapeutic effects that might be expected on a subset of individuals showing both cognitive complaints and signs of copper imbalance.