The extract of Azadirachta indica (AI) leaves has been explored as a green inhibitor for mild steel (MS) in 5.0 m hydrochloric acid by computational (DFT, Langmuir/Freundlich adsorption, frontier molecular orbital, and molecular dynamics simulation) and experimental (polarization, gravimetric, gasometric, and impedance) techniques. Corroded surfaces have been investigated by metallurgical microscopy and SEM techniques. The impedance parameters and inhibition efficiency were found to increase with AI extract concentration, the latter from 50.64% to 89.25%. Various theoretical parameters, such as electronic charge in the HOMO/LUMO, Fukui function, metal−inhibitor interaction energy (−22.12 kJ/mol), adsorption energy (7.86 kJ/mol), back-donation energy, chemical potential (3.95 eV), and global hardness (1.75 eV), imply high adsorption of AI extract (flavonoid as major constituent) on MS. SEM and metallurgical imaging techniques have proved the growth of a uniform barrier film on the surface of MS with increasing AI extract concentration. The numbers and intensities of pits and cracks decrease with increasing AI extract concentration. A maximum of 89.25% inhibitory efficiency was shown by AI. Wastewater from gravimetric experiments was examined for biocompatibility and biodegradability, and was found within the permissible range.