The gastric pathogen Helicobacter pylori encodes two carbonic anhydrases (CAs, EC 18.104.22.168), an α- and a β-class one, hpαCA and hpβCA, crucial for its survival in the acidic environment from the stomach. Sulfonamides, strong inhibitors of these enzymes, block the growth of the pathogen, in vitro and in vivo. Here we report the inhibition of the two H. pylori CAs with inorganic and complex anions and other molecules interacting with zinc proteins. hpαCA was inhibited in the low micromolar range by diethyldithiocarbamate, sulfamide, sulfamic acid, phenylboronic acid, and in the submillimolar one by cyanide, cyanate, hydrogen sulfide, divanadate, tellurate, perruthenate, selenocyanide, trithiocarbonate, iminodisulfonate. hpβCA generally showed a stronger inhibition with most of these anions, with several low micromolar and many submillimolar inhibitors detected. These inhibitors may be used as leads for developing anti-H. pylori agents with a diverse mechanism of action compared to clinically used antibiotics.