A library of structurally diverse N-((4-sulfamoylphenyl)carbamothioyl) amides was synthesized by selective acylation of easily accessible 4-thioureidobenzenesulfonamide with various aliphatic, benzylic, vinylic and aromatic acyl chlorides under mild conditions. Inhibition of three α-class cytosolic human (h) carbonic anhydrases (CAs) (EC 4.2.1.1); that is, hCA I, hCA II and hCA VII and three bacterial β-CAs from Mycobacterium tuberculosis (MtCA1-MtCA3) with these sulfonamides was thereafter investigated in vitro and in silico. Many of the evaluated compounds displayed better inhibition against hCA I (KI = 13.3–87.6 nM), hCA II (KI = 5.3–384.3 nM), and hCA VII (KI = 1.1–13.5 nM) compared with acetazolamide (AAZ) as the control drug (KI values of 250, 12.5 and 2.5 nM, respectively, against hCA I, hCA II and hCA VII). The mycobacterial enzymes MtCA1 and MtCA2 were also effectively inhibited by these compounds. MtCA3 was, on the other hand, poorly inhibited by the sulfonamides reported here. The most sensitive mycobacterial enzyme to these inhibitors was MtCA2 in which 10 of the 12 evaluated compounds showed KIs (KI, the inhibitor constant) in the low nanomolar range.