Multidrug-resistant (MDR) Gram-negative bacteria are the top-priority pathogens to be eradicated. Drug repurposing (e.g., the use of non-antibiotics to treat bacterial infections) may be helpful to overcome the limitations of current antibiotics. Zidovudine (azidothymidine, AZT), a licensed oral antiviral agent, is a leading repurposed drug against MDR Gram-negative bacterial infections. However, the rapid emergence of bacterial resistance due to long-term exposure, overuse, or misuse limits its application, making it necessary to develop new alternatives. In this study, we investigated the efficacy of ciclopirox (CPX) as an alternative to AZT. The minimum inhibitory concentrations of AZT and CPX against MDR Gram-negative bacteria were determined; CPX appeared more active against β-lactamase-producing Escherichia coli, whereas AZT displayed no selectivity for any antibiotic-resistant strain. Motility assays revealed that β-lactamase-producing Escherichia coli strains were less motile in nature and more strongly affected by CPX than a parental strain. Resistance against CPX was not observed in E. coli even after 25 days of growth, whereas AZT resistance was observed in less than 2 days. Moreover, CPX effectively killed AZT-resistant strains with different resistance mechanisms. Our findings indicate that CPX may be utilized as an alternative or supplement to AZT-based medications to treat opportunistic Gram-negative bacterial infections.