Step 1: Identify zinc-containing minerals.
Zinc occurs in nature mainly in the form of its ores and minerals such as zinc blende, calamine, and willemite.
Step 2: Analyze each option.
(A) Willemite: It is zinc silicate $(Zn_2SiO_4)$ and is an important ore of zinc.
(B) Corundum: It is aluminium oxide $(Al_2O_3)$.
(C) Azurite: It is basic copper carbonate.
(D) Malachite: It is also a copper carbonate mineral.
Step 3: Conclusion.
Willemite is the mineral that contains zinc.