(1) Background: Mental health issues in older adults, particularly cognitive impairment and depression, can affect nutritional status. This study investigates the prevalence of malnutrition among community-dwelling older adults at risk of social exclusion and dependency in Lebanon and its association with cognitive impairment and depression. (2) Methods: This cross-sectional study used secondary data from the TEC-MED project, involving 1410 older adults aged 60 and above in Beirut. Nutritional status was assessed with the Mini Nutritional Assessment _Short Form (MNA_SF), cognitive impairment with the AD8 Dementia Screening Interview, and depression with the Geriatric Depression Scale (GDS-15). (3) Results: 87.2% of participants were at risk of malnutrition, and 2.5% were malnourished. Cognitive impairment was present in 82.2% of the sample and 45% experienced moderate to severe depression. Malnourished individuals had significantly higher rates of cognitive impairment (96.7% vs. 57.8%) and depression (85.7% vs. 23.2%). Significant associations were found between the risk of malnutrition, decreased food intake, cognitive impairment, and depression; however, no significant association was found with BMI. Logistic regression analysis indicated that older age, cognitive impairment, and depression were significant predictors of malnutrition, while having a caregiver was protective. (4) Conclusions: The high prevalence of risk of malnutrition among vulnerable older adults with cognitive impairment and depression underscores the need for policies integrating nutritional screening into routine health check-ups for older adults.