To extend our screening for novel antimycobacterial molecules, we have designed, synthesized, and biologically evaluated a library of 14 new hydrazide derivatives containing 1,3,4-oxadiazole core. A variety of mycobacterial strains, including some drug-resistant strains, were tested for antimycobacterial activity. Among the compounds tested, five showed high antimycobacterial activity (MIC values of 8 μg/mL) against M. tuberculosis H37Ra attenuated strain, and two derivatives were effective (MIC of 4 µg/mL) against pyrazinamide-resistant strains. Furthermore, the novel compounds were tested against the fungal C. albicans strain, showing no antimycotic activity, and thus demonstrating a good selectivity profile. Notably, they also exhibited low cytotoxicity against human SH-SY5Y cells. The molecular modeling carried out suggested a plausible mechanism of action towards the active site of the InhA enzyme, which confirmed our hypothesis. In conclusion, the active compounds were predicted in silico for ADME properties, and all proved to be potentially orally absorbed in humans.