The enzyme carboxypeptidase is well-known for its utilization of a zinc ion as a cofactor in its catalytic mechanism. The zinc ion plays a crucial role in the hydrolysis of peptide bonds, the reaction facilitated by carboxypeptidase. The presence of zinc allows for proper stabilization of water molecules which are necessary in the catalysis, making the hydrolysis of the peptide bond effective. This zinc dependency categorizes carboxypeptidase as a metalloenzyme.

Therefore, the correct answer is:

Option A: Zinc

Other options mentioned, such as Niacin, Flavin, and Haem, serve as cofactors for different enzymes. For example, Niacin is involved in the formation of NAD+ (Nicotinamide adenine dinucleotide) which acts as an electron carrier in many enzymatic reactions. Flavins (like FMN and FAD) are involved in a myriad of oxidation-reduction (redox) reactions. Haem, found in hemoglobin and cytochromes, also plays crucial roles primarily in electron transfer processes and oxygen transport. These are not associated with the functioning of carboxypeptidase, which specifically requires zinc for its enzymatic activity.