A series of mono- and heteronuclear platinum(II) and zinc(II) complexes with 4,4′,4″-tri-tert-butyl-2,2′:6′,2″-terpyridine ligand were synthesized and characterized. The DNA and protein binding properties of [ZnCl2(terpytBu)] (C1), [{cis-PtCl(NH3)2(μ-pyrazine)ZnCl(terpytBu)}](ClO4)2 (C2), [{trans-PtCl(NH3)2(μ-pyrazine)ZnCl(terpytBu)}](ClO4)2 (C3), [{cis-PtCl(NH3)2(μ-4,4′-bipyridyl)ZnCl(terpytBu)}](CIO4)2 (C4) and [{trans-PtCl(NH3)2(μ-4,4′-bipyridyl)ZnCl(terpytBu)}](CIO4)2 (C5) (where terpytBu = 4,4′,4″-tri-tert-butyl-2,2′:6′,2″-terpyridine), were investigated by electronic absorption, fluorescence spectroscopic, and molecular docking methods. Complexes featuring transplatin exhibited lower Kb and Ksv constant values compared to cisplatin analogs. The lowest Ksv value belonged to complex C1, while C4 exhibited the highest. Molecular docking studies reveal that the binding of complex C1 to DNA is due to van der Waals forces, while that of C2–C5 is due to conventional hydrogen bonds and van der Waals forces. The tested complexes exhibited variable cytotoxicity toward mouse colorectal carcinoma (CT26), human colorectal carcinoma (HCT116 and SW480), and non-cancerous mouse mesenchymal stem cells (mMSC). Particularly, the mononuclear C1 complex showed pronounced selectivity toward cancer cells over non-cancerous mMSC. The C1 complex notably induced apoptosis in CT26 cells, effectively arrested the cell cycle in the G0/G1 phase, and selectively down-regulated Cyclin D.