Excessive use of antimicrobial medications including antibiotics has led to the emerging menace of antimicrobial resistance, which, as per the World Health Organization (WHO), is among the top ten public health threats facing humanity, globally. This necessitates that innovative technologies be sought that can aid in the elimination of pathogens and hamper the spread of infections. Zinc oxide (ZnO) has multifunctionality owing to its extraordinary physico-chemical properties and functionality in a range of applications. In this research, ZnO nanoparticles (NPs) were synthesized from zinc nitrate hexahydrate, by a green synthesis approach using Cymbopogon citratus extract followed by characterization of the NPs. The obtained X-ray diffraction peaks of ZnO NPs matched with the standard JCPDS card (no. 89-510). The particles had a size of 20-24 nm, a wurtzite structure with a high crystallinity, and hexagonal rod-like shape. UV-Vis spectroscopy revealed absorption peaks between 369 and 374 nm of ZnO NPs synthesized from C. citratus extract confirming the formation of ZnO. Fourier transform infrared confirmed the ZnO NPs as strong absorption bands were observed in the range of 381-403 cm^-1 corresponding to Zn-O bond stretching. Negative values of the highest occupied molecular orbital-lowest unoccupied molecular orbital for ZnO NPs indicated the good potential to form a stable ligand-protein complex. Docking results indicated favorable binding interaction between ZnO and DNA gyrase subunit b with a binding energy of -2.93 kcal/mol. ZnO NPs at various concentrations inhibited the growth of Escherichia coli and Staphylococcus aureus. Minimum inhibitory concentration values of ZnO NPs against E. coli and S. aureus were found to be 92.07 ± 0.13 and 88.13 ± 0.35 μg/mL, respectively, at a concentration of 2 mg/mL. AO/EB staining and fluorescence microscopy revealed the ability of ZnO NPs to kill E. coli and S. aureus cells. Through the findings of this study, it has been shown that C. citratus extract can be used in a green synthesis approach to generate ZnO NPs, which can be employed as alternatives to antibiotics and a tool to eliminate drug-resistant microbes in the future.