In this study, a series of new heteroleptic silver(I), nickel(II), and copper(II) complexes of the type [M(L1–3)(Cfx)n] (1–9), where L1–3 = N4-substituted thiosemicarbazones (TSCs), Cfx = ciprofloxacin, M = Ag(I), Ni(II), or Cu(II), and n = 1 or 2, have been synthesized and characterized by spectral methods. The spectral data of the complexes suggest bidentate behavior of the TSC ligand, which coordinate with metal ion through thione sulphur and hydrazine nitrogen atoms, and neutral bidentate behavior of the ciprofloxacin drug that coordinates with metal ion through pyridone oxygen and one of the carboxylate oxygen atoms. The structural properties of the silver(I) complexes (1–3) were studied by density functional theory calculations, which indicate the distorted tetrahedral geometry with lower energy gap for complex 3. All the heteroleptic complexes were screened for their in vitro anti-proliferative activity against four cancerous (lung [A549], estrogen negative [MDA-MB-231], estrogen positive [MCF-7] and Henrietta's cancer cells [HeLa]), and one non-cancerous (non-tumorigenic human breast epithelial cell line [MCF-10a]) cell lines by MTT reduction assay. The obtained results revealed the lower activity of silver(I) complexes and higher activity of copper(II) complexes against the tested cancer cell lines. The complexes 6 and 9 induce apoptosis in MDA-MB-231 cells, which was evidenced by acridine orange/ethidium bromide staining method. The molecular docking studies revealed hydrogen bonding and hydrophobic interactions between the complexes and the epidermal growth factor receptor. The in silico analysis of the complexes for Lipinski's “rule of five” and absorption, distribution, metabolism, and excretion properties predicted the drug-likeness of the synthesized complexes.