We have synthesized and characterized a novel copper(II) complex of the fluoroquinolone antibacterial drug N-propyl-norfloxacin (Hpr-norf) in the presence of 1,10-phenanthroline (Phen) and studied its biological properties as antitumor antibiotic and antimicrobial agent. Human acute myeloid leukemia cell line HL-60, MTT assay, and Trypan blue assay were used to test the antileukemic, the cell viability, and the structural integrity of the cell membrane and cell proliferation properties of (chloro)(Phen)( N-propyl-norfloxacinato)copper(II) (complex 1), respectively. We found that the proliferation rate and viability of HL-60 cells decreased after treatment with complex 1, leading to cell death through apoptosis in a time-dependent manner. The antimicrobial activity of complex 1 has been tested, revealing an increased potency in comparison to the free Hpr-norf. Complex 1 proved to be capable of acting as an independent nuclease by inducing nicking of supercoiled pUC19 plasmid. Our results suggest that 1 may provide a valuable tool in cancer chemotherapy.