A new Cu^II complex (1) was synthesized by reacting 4-chlorobenzoic acid, benzimidazole and metal salt using ethanol–water (1:1 v/v) as a solvent at room temperature. The complex was characterized by single-crystal X-ray analysis, FTIR and UV—vis spectroscopy. A distorted square pyramidal geometry of the Cu^II center was observed from the single-crystal X-ray study, which also revealed that the uncoordinated oxygen atom of the carboxylate anions forms intermolecular hydrogen bonds with the N–H groups of the benzimidazole ligands. The Hirshfeld analysis results revealed that the molecular packing of 1 is mainly controlled by O...H (12.7%), Cl...H (16.4%), C...H (24.4%) and H...H (31.1%) contacts. Density functional theory (DFT) calculations were performed to compute the HOMO–LUMO energy gap and electrostatic potential map for the charge transfer regions within the molecule and identify the possible electrophilic and nucleophilic regions of the molecule. A number of reactivity parameters calculated on the basis of E_HOMO and E_LUMO show its significant polarizability and reactive nature. Complex 1 was also examined and screened for its potential antibacterial effect using the agar well diffusion method. The newly synthesized complex showed an effective and higher killing rate of the microbes in antibacterial testing compared to the parent ligand. The Cu^II complex (1) showed an enhanced inhibitory activity against P. aeruginosa and equally demonstrated greater binding affinity with DNA gyrase (1KIJ) compared to its ligands according to the molecular docking studies.