New azidosulfonamide–chalcone derivatives were designed and synthesized. Their structures were elucidated by 1H and 13CNMR spectral analyses, in addition to elemental analyses. The synthesized derivatives were tested for their antimicrobial activity against a wide variety of Gram-positive, Gram-negative, and fungal strains. Three azidosulfonamide–chalcones showed relatively broad activity against tested strains. Two compounds exhibited eminent antibacterial activity toward S. aureus, M. luteus, and S. marcens (better than ampicillin trihydrate). The synthesized compounds exhibited moderate activity against K. pneumonia and a lower ability to inhibit E. coli growth. Among six tested fungal species, the most potent derivatives demonstrated strong activity toward only two of the fungal strains (T. rubrum and G. candidum). Assessment of drug-likeness, bioavailability, and promiscuity indicated that the compounds are viable drug candidates. In silico molecular docking analysis revealed that the synthesized azidosulfonamide–chalcones successfully occupied pterin-binding site of the dihydropteroate synthase (DHPS), implying that the prepared compounds could exert their activity by the inhibition of the microbial DHPS enzyme. These results provided essential information for the prospective design of more effective antimicrobial compounds.