Antibiotic resistance is a major problem of tuberculosis treatment. This provides the stimulus for the search of novel molecular targets and approaches to reduce or forestall resistance emergence in Mycobacterium tuberculosis. Earlier, we discovered a novel small-molecular inhibitor among 3-phenyl-5-(1-phenyl-1H-[1,2,3]triazol-4-yl)-[1,2,4]oxadiazoles targeting simultaneously two enzymes—mycobacterial leucyl-tRNA synthetase (LeuRS) and methionyl-tRNA synthetase (MetRS), which are promising molecular targets for antibiotic development. Unfortunately, the identified inhibitor does not reveal antibacterial activity toward M. tuberculosis. This study aims to develop novel aminoacyl-tRNA synthetase inhibitors among this chemical class with antibacterial activity toward resistant strains of M. tuberculosis. We performed molecular docking of the library of 3-phenyl-5-(1-phenyl-1H-[1,2,3]triazol-4-yl)-[1,2,4]oxadiazole derivatives and selected 41 compounds for investigation of their inhibitory activity toward MetRS and LeuRS in aminoacylation assay and antibacterial activity toward M. tuberculosis strains using microdilution assay. In vitro screening resulted in 10 compounds active against MetRS and 3 compounds active against LeuRS. Structure-related relationships (SAR) were established. The antibacterial screening revealed 4 compounds active toward M. tuberculosis mono-resistant strains in the range of concentrations 2–20 mg/L. Among these compounds, only one compound 27 has significant enzyme inhibitory activity toward mycobacterial MetRS (IC50 = 148.5 µM). The MIC for this compound toward M. tuberculosis H37Rv strain is 12.5 µM. This compound is not cytotoxic to human HEK293 and HepG2 cell lines. Therefore, 3-phenyl-5-(1-phenyl-1H-[1,2,3]triazol-4-yl)-[1,2,4]oxadiazole derivatives can be used for further chemical optimization and biological research to find non-toxic antituberculosis agents with a novel mechanism of action.