Helicobacter pylori infections are highly common amongst the global population. Such infections have been shown to be the cause of gastric ulcers and stomach carcinoma and, unfortunately, most cases are asymptomatic. Standard treatment requires antibiotics such as metronidazole or azithromycin to which many strains are now resistant. Mentha species have been used as a natural treatment for gastrointestinal diseases throughout history and essential oils (EOs) derived from these plants show promising results as potential antimicrobial agents. In this study, EOs obtained from the leaves and flowers of five cultivars of Mentha × piperita and M. spicata were examined by GC-MS. The investigated mints are representatives of four chemotypes: the menthol chemotype (M. × piperita ‘Multimentha’ and M. × piperita ‘Swiss’), the piperitenone oxide chemotype (M. × piperita ‘Almira’), the linalool chemotype (M. × piperita ‘Granada’), and the carvone chemotype (M. spicata ‘Moroccan’). The chemical composition of EOs from mint flowers and leaves was comparable with the exception of the Swiss cultivar. Menthol was the most abundant component in the leaves while menthone was highest in flowers. The H. pylori ATCC 43504 reference strain and 10 other H. pylori clinical strains were examined for their sensitivity to the EOs in addition to their major monoterpenoid components (menthol, menthone, carvone, dihydrocarvone, linalool, 1,8-cineole, and limonene). All tested mint EOs showed inhibitory activity against both the reference H. pylori ATCC 43504 strain (MIC 15.6–31.3 mg/L) and clinical H. pylori strains (MIC50/90 31.3–250 mg/L/62.5–500 mg/L). Among the reference monoterpenes, menthol (MIC50/90 7.8/31.3 mg/L) and carvone (MIC50/90 31.3/62.5 mg/L) had the highest anti-H. pylori activity, which also correlated with a higher activity of EOs containing these compounds (M. × piperita ‘Swiss’ and M. spicata ‘Moroccan’). A synergistic and additive interaction between the most active EOs/compounds and antibiotics possibly points to a new plant-based anti-H. pylori treatment.