This study examined the relationship between adherence to the Mediterranean diet (MD), dietary and vitamin intake, physical activity, and body composition in young adults. A total of 145 Spanish university students (34 women and 111 men) were included in this cross-sectional study, with a mean body mass index (BMI) of 23 kg/m2. MD adherence was assessed using the Mediterranean Diet Adherence Screener (MEDAS). Dietary intake was evaluated through a three-day food record, physical activity using the International Physical Activity Questionnaire (IPAQ), and body composition by bioelectrical impedance analysis. Overall adherence to the MD was moderate. Participants with high MD adherence showed significantly lower body weight (p < 0.05), BMI (p < 0.01), fat mass (p < 0.05), and fat mass percentage (p < 0.05) compared with those with low adherence. Energy, protein, and carbohydrate intake per kilogram of body weight were higher (p < 0.05) in the high-adherence group. Fiber intake was greater (p < 0.001) among those with higher MD adherence. Adherence to the MD was also associated with higher intakes of vitamins C (p < 0.05), E (p < 0.05), retinol equivalents (p < 0.05), and carotenoids (p < 0.001). MD adherence was inversely correlated (r = −0.24, p < 0.01) with body weight and BMI. Fiber intake showed positive correlations with several water-soluble vitamins, particularly folate (p < 0.001). In conclusion, higher adherence to the MD among university students was associated with healthier body composition and improved vitamin intake adequacy, independently of physical activity. These findings support the promotion of the MD as an effective nutritional strategy to enhance micronutrient intake and overall diet quality in young adults.