The novel neutral mononuclear copper(II) complexes with the quinolone antibacterial drugs ciprofloxacin in the presence of the nitrogen donor heterocyclic ligand of terpyridine have been synthesized and characterized by elemental analysis, reflectance spectra, IR and mass spectroscopy. The antibacterial activities of the newly synthesized compounds were evaluated and correlated with their physicochemical properties. Results revealed that the tested compounds exhibited better inhibitory activities than the reference antibacterial quinolone drugs against Gram (+ve) and Gram (−ve) bacteria. The coordination compounds can act as catalysts for the dismutation of superoxide anion radicals (O2·-). The detection of the rate constant of the reaction of superoxide ion with nitro blue tetrazolium (NBT) is inhibited by superoxide dismutase (SOD). The interaction of the complex with DNA was investigated using viscosity, absorption titration and DNA melting temperature techniques. The results indicate that the complexes bind to DNA with intercalative mode and they have rather high DNA-binding constants. DNA-cleavage study showed better cleaving ability of the complexes compare to metal salt and standard drugs.