First, remember that:
When we put the electrons using the Aufbau Principle, something different happens after Argon element. At argon, the 3s and 3p levels are full, but rather than filling up the 3d levels next, the 4s level fills instead to give potassium (K) and then calcium (Ca). Only after that the 3d levels are filled. The elements in the Periodic Table which correspond to the d levels filling are known as d block elements.
ANSWER:
The definition of a transition metal is that:
A transition metal is one that forms one or more stable ions which have incompletely filled d orbitals.
Based in this definition, we notice that Zinc has the following electronic structure:
When Zinc forms ions, it always loses the two 4s electrons to give a +2 ion with the electronic structure Ar 3d10. As we can see, this ion has completely filled d orbitals, so it can't be considered as a transition metal since it doesn't meet the given definition.