This study examined associations between muscle strength and mental health among 2,652 elderly Koreans who participated in the 2015 and 2017 Korea National Health and Nutrition Examination Survey. We measured absolute handgrip strength and calculated handgrip strength relative to body mass index. Dynapenia criteria followed that of the Asian Working Group for Sarcopenia. Questionnaires were used to assess mental health indicators including suicidal ideation, depressed mood, and stress status. Among participants, 18.6%, 14.9%, and 6.7% reported stress, depressed mood, and suicidal ideation, respectively. Dynapenia prevalence was 25.1%. Adjusted odds ratios of stress, depressed mood, and suicidal ideation for men with dynapenia were 2.15, 2.30, and 2.11, respectively. Significant associations were absent among women. For men, handgrip strength and relative handgrip strength were inversely associated with risk of stress, depressed mood, and suicidal ideation. For women, handgrip strength and relative handgrip strength were inversely associated with the risk of stress, but not of depressed mood and suicidal ideation. In conclusion, all muscle-strength indices were associated with mental health risks among older men. In older women, low handgrip strength and relative handgrip strength were associated with increased stress. Muscle strength could be a clinical marker of poor mental health in older adults.