A new series of 1,3,4-thiadiazoles was synthesized by the reaction of methyl 2-(4-hydroxy-3-methoxybenzylidene) hydrazine-1-carbodithioate (2) with selected derivatives of hydrazonoyl halide by grinding method at room temperature. The chemical structures of the newly synthesized derivatives were resolved from correct spectral and microanalytical data. Moreover, all synthesized compounds were screened for their antimicrobial activities using Escherichia coli, Pseudomonas aeruginosa, Proteus vulgaris, Bacillus subtilis, Staphylococcus aureus, and Candida albicans. However, compounds 3 and 5 showed significant antimicrobial activity against all tested microorganisms. The other prepared compounds exhibited either only antimicrobial activity against Gram-positive bacteria like compounds 4 and 6, or only antifungal activity like compound 7. A molecular docking study of the compounds was performed against two important microbial enzymes: tyrosyl-tRNA synthetase (TyrRS) and N-myristoyl transferase (Nmt). The tested compounds showed variety in binding poses and interactions. However, compound 3 showed the best interactions in terms of number of hydrogen bonds, and the lowest affinity binding energy (−8.4 and −9.1 kcal/mol, respectively). From the in vitro and in silico studies, compound 3 is a good candidate for the next steps of the drug development process as an antimicrobial drug.