Background: Food subsidies for healthier foods and higher taxes for less healthy alternatives have been increasingly used to promote a healthy diet. Yet, some have argued that the fiscal burden on unhealthy products would fall disproportionately on the worse-off, raising equity concerns. This study estimates the association between income and the consumption of key food groups linked to the Mediterranean diet in the adult Portuguese population. Methods: We used data from the Portuguese National Food, Nutrition and Physical Activity Survey (IAN-AF 2015–2016), which observed the daily diet of individuals aged above 18 and below 79 years old (n = 3242). Logistic regression models were used to estimate the magnitude of the association between self-reported household income categories and consumption of foods related to the Mediterranean diet (fish, vegetables, fruits and legumes), and not (sweets, sugar-sweetened beverages, cakes & pastries and processed meats). Stratified analyses were performed by education and age categories. Results: We observed that the intake of fish (35.8 vs 38.8 g p = 0.02), vegetables (146.7 vs 166.2 g p < 0.01), and fruits (119.8 vs 150.1 g p < 0.01) was positively related to income, with a clear gradient for the two latter. Yet, the positive income-consumption link for fish was only observed among low-educated people, and the one for legumes among high educated and youths. Conversely, the consumption of most non-Mediterranean foods was not positively related to income categories, with the exception of sweets (34.8 vs 31.8 g p = 0.01) and cakes (26.4 vs 21.4 g p < 0.01) (more prevalent among the better-off). Conclusions: The consumption of healthy food is mostly consistently related to income, contrary to the intake of unhealthy ones. It may well be, therefore, that subsidies to healthy foods could allow access to the worse-off while taxing unhealthy food will not impose a disproportionate burden on them.