Taste perception plays an undisputed role in food choice, preference, and intake. Recent literature suggests that individual diet and taste sensitivity may have a reciprocal relationship, with evidence highlighting that specific diets can alter taste sensitivities. Commensurate with an increase in the prevalence of plant-based diets is the importance of investigating if following a vegetarian or vegan diet is associated with altered taste sensitivities. In this study, the taste detection thresholds for six compounds (i.e., sweet—sucrose, salty—sodium chloride, sour—citric acid, umami—monosodium glutamate, MSG, bitter—caffeine, and metallic—iron II sulphate heptahydrate) were measured for a total of 80 healthy, New Zealand European females aged 18–45 years old, who were categorised as 22 vegans, 23 vegetarians, and 35 omnivores. Each participant’s detection thresholds to these compounds were measured across two sessions, using an ascending Method of Limits with two-alternative-forced-choice presentations. The threshold data were analysed using both multivariate (i.e., principal component analysis) and univariate (i.e., ANCOVA) techniques to assess differences across the three types of diet. Multivariate analysis suggested that the omnivore group had distinct taste sensitivity patterns across the six compounds compared to the vegetarian or vegan group, which were characterised by relatively heightened sensitivity to metallic and lowered sensitivity to sweetness. Furthermore, the vegetarian group was shown to have a significantly lower detection threshold to bitterness (i.e., caffeine) relative to the other two groups (p < 0.001). While future study is required to investigate the cause–effect relationship between individual diet and taste sensitivities, the present study provides a systematic evaluation of taste sensitivities of individuals following distinct diets. This information may be valuable to future gustatory research as well as to food manufacturers.