A new hexanuclear Zn(II) complex with the ligand 2,2'-(piperazine-1,4-diyl)bis(ethan-1-amine), [L3Zn6(OH)6][ClO4]6·3MeOH·7H2O, was synthesized. The crystal structure of this complex showed that each Zn atom is in a distorted tetrahedral coordination environment, surrounded by two nitrogen atoms from each ligand and two hydroxide groups, each of which bridges to another Zn atom. The anticancer activities of the ligand and its metal complex against the breast cancer cell line (MCF-7) indicated that the zinc complex had a greater anticancer activity. The free ligand and its metal complex were evaluated for antioxidant activity using the DPPH scavenging method. In addition, the antibacterial activities of both compounds were screened against Gram-positive (Staphylococcus aureus) and Gram-negative (Escherichia coli) bacteria. The interaction of these compounds with DNA and AChE was also investigated using molecular docking.