There seems to be no evidence that zinc supplements would cause hypocalcemia in humans.
According to the study Effect of zinc supplements on the intestinal absorption of calcium (PubMed, 1987), calcium and zinc may inhibit each other's absorption:
the high zinc intake decreased the intestinal absorption of calcium
during a low calcium intake but not during a normal calcium intake
But:
Office of Dietary Supplements by NIH.gov does not mention hypocalcemia as a possible side effect of zinc supplements.
Drugs.com does not mention any interaction between zinc and calcium supplements.
Also, the mentioned claim from Wikipedia article lacks any reference.
In rats, zinc supplements can cause acute hypocalcemia (PubMed, 1981), but I'm not aware of any association of this study with humans.