Based on the importance of the design and synthesis of transition metal complexes with noncovalent DNA/protein-binding abilities in the field of metallo pharmaceuticals, a new mononuclear ternary copper(II) complex with mixed ligands of diethylenetriamine (dien) and picrate anion (pic), identified as [Cu(dien)(pic)](pic), was synthesized and characterized by elemental analysis, molar conductivity measurement, infrared spectrum, electronic spectral studies, and single-crystal X-ray diffractometry. The structure analysis reveals that the copper(II) complex crystallizes in the monoclinic space group P21 /c, and the copper(II) ion has a distorted square pyramidal coordination geometry. A two-dimensional supramolecular structure is formed through hydrogen bonds. The DNA/bovine serum albumin (BSA)-binding properties of the complex are explored, indicating that the complex can interact with herring sperm DNA via intercalation mode and bind to BSA responsible for quenching of tryptophan fluorescence by static quenching mechanism. The in vitro anticancer activity shows that the copper(II) complex is active against the selected tumor cell lines.