Bacteria expressing New Delhi metallo-β-lactamase-1 (NDM-1) can hydrolyze β-lactam antibiotics (penicillins, cephalosporins, and carbapenems) and, thus, mediate multidrug resistance. The worldwide dissemination of NDM-1 poses a serious threat to public health, imposing a huge economic burden in the development of new antibiotics. Thus, there is an urgent need for the identification of novel NDM-1 inhibitors from a pool of already-known drug molecules. Here, we screened a library of FDA-approved drugs to identify novel non-β-lactam ring-containing inhibitors of NDM-1 by applying computational as well as in vitro experimental approaches. Different steps of high-throughput virtual screening, molecular docking, molecular dynamics simulation, and enzyme kinetics were performed to identify risedronate and methotrexate as the inhibitors with the most potential. The molecular mechanics/generalized Born surface area (MM/GBSA) and molecular dynamics (MD) simulations showed that both of the compounds (risedronate and methotrexate) formed a stable complex with NDM-1. Furthermore, analyses of the binding pose revealed that risedronate formed two hydrogen bonds and three electrostatic interactions with the catalytic residues of NDM-1. Similarly, methotrexate formed four hydrogen bonds and one electrostatic interaction with NDM-1’s active site residues. The docking scores of risedronate and methotrexate for NDM-1 were –10.543 kcal mol−1 and −10.189 kcal mol−1, respectively. Steady-state enzyme kinetics in the presence of risedronate and methotrexate showed a decreased catalytic efficiency (i.e., kcat/Km) of NDM-1 on various antibiotics, owing to poor catalytic proficiency and affinity. The results were further validated by determining the MICs of imipenem and meropenem in the presence of risedronate and methotrexate. The IC50 values of the identified inhibitors were in the micromolar range. The findings of this study should be helpful in further characterizing the potential of risedronate and methotrexate to treat bacterial infections.