The structural and electronic properties of the metallic hcp phase of Zn in the bulk, monolayer, bilayer, and quantum dot limits have been studied by using total energy calculations. From our calculated density of states and electronic band structure, in agreement with previous work, bulk hybridization of the Zn-4s, 3p, and 3d orbitals is obtained. Furthermore, we found that this orbital hybridization is also obtained for the monolayer, bilayer, and quantum dot systems. At the same time, we found that the Zn monolayer and bilayer systems show electronic properties characteristic of lamellar systems, while the quantum dot system shows the behavior predicted for a 0D system.