Adequate sodium and potassium intake, along with adherence to the Mediterranean diet (MedDiet), are key factors for preventing hypertension and cerebrovascular diseases. However, data on the consumption of these nutrients within the MedDiet are scarce. This cross-sectional study aims to assess the association between MedDiet adherence and sodium/potassium intake in the MIND-Matosinhos randomized controlled trial, targeting Portuguese adults at a high risk of dementia. Good adherence to the MedDiet was defined using the Portuguese Mediterranean Diet Adherence Screener questionnaire (≥10 points), and both sodium/potassium intakes were estimated from 24-hour urine collections. The association between MedDiet adherence and these nutrients’ intake (dichotomized by the median) was quantified by calculating odds ratios (OR) and respective 95% confidence intervals (95% CI) using a logistic regression. A total of 169 individuals (60.9% female; median age: 70 years; range: 36–85 years) were included. Good adherence to the MedDiet was observed among 18.3% of the sample. After adjusting for sex, age, education and using antihypertensive drugs, good MedDiet adherence was associated with higher sodium (OR = 3.11; 95% CI: 1.27–7.65) and potassium intake (OR = 9.74; 95% CI: 3.14–30.26). Increased adherence to the MedDiet may contribute to a higher potassium intake but seems to have limited effects on the adequacy of sodium levels.