Objectives The aim of the current study was to assess the associations between dynapenia and the onset and persistence of depression and anxiety among older adults. Methods This prospective cohort study enrolled community-living older adults (N = 5271; 51.1% females) aged ≥ 50 years (mean age = 63.2, standard deviation = 9.0) from The Irish Longitudinal Study on Aging (TILDA), Ireland. At baseline, participants completed a handgrip assessment. Depression was defined by a score ≥ 16 in the Center of Epidemiology Studies Depression (CES-D) tool and anxiety was considered when participants scored ≥ 8 on the anxiety section of the Hospital Anxiety and Depression Scale (HADS). Outcomes were incident and persistent depression and anxiety at two years follow-up. Multivariable logistic regression models were built for each outcome. Results After controlling for age, sex, education, marital status, employment status, smoking, body mass index, number of chronic conditions, physical activity, and cognitive function, low handgrip strength indicative of dyapenia (< 30 Kg for men and < 20 Kg for women) was associated with a greater likelihood for incident depressive (OR = 1.44; 95%CI: 1.08–1.92) as well as for persistent depressive (OR = 1.61; 95% CI: 1.01–2.58) and anxiety (OR = 1.61; 95% CI: 1.20–2.14) symptoms. Conclusions Dynapenia was associated with a higher odds of developing depressive symptoms as well as a greater likelihood to persistent depressive and anxiety symptoms among older adults. Our data suggest that interventions targeting muscle strength may prevent the onset of late-life depression and also may hold promise as novel therapeutic opportunities for depression and anxiety in later life.