Nutrition intake plays a pivotal role in chewing difficulty (CD). This cross-sectional descriptive study aims to explore the associations between CD and the dietary intake of calcium (Ca), vitamin D, and magnesium (Mg) in adults aged 65 and older, utilizing data from the 8th Korea National Health and Nutrition Examination Survey (2020–2021). The chewing function was assessed using a 5-point scale questionnaire that inquired about discomfort experienced during mastication. “Very uncomfortable” and “uncomfortable,” two of the five response options, were categorized as being indicative of CD. Dietary intake was assessed through 24 h dietary recall interviews, and nutrient calculations were based on the 10th revised edition of the Korean Food Composition Table. Data (N = 2942) were analyzed using descriptive statistics and multi-logistic regression analyses in a composite sample plan file. Among the 2942 subjects, groups with insufficient daily nutrient intake had significantly higher odds ratios (ORs) for CD compared to their counterparts. In men, the ORs for Ca (1.56), Mg (1.75), and the combined intake of Mg (1.64) with Ca were elevated. In women, the ORs for Ca (1.74), Mg (1.53), and the combined intake of Mg (1.43) with Ca showed similar trends. After adjusting for age, family income, and family size variables, men’s ORs for Mg (1.55) and the combined intake of Mg (1.55) with Ca remained elevated, while women’s OR for Ca (1.58), Mg (1.42), and the combined intake of Mg (1.34) with Ca remained significant. Dietary vitamin D intake did not significantly impact the OR for CD. After adjusting for natural tooth numbers, self-perceived oral health, and obesity, no significant association was found between CD and these nutrients. In conclusion, this study underscores the importance of promoting the recommended daily intake of magnesium alongside dietary calcium to address CD.