The benefits of physical activity for the physical health of individuals are well documented. Less is known about the benefits of physical activity for mental health. This paper explores the associations between physical activity and positive mental health and mental health problems. The paper utilises data collected from a representative sample of 10–17-year-old adolescents in Ireland. Physical activity in the study is measured using moderate-to-vigorous physical activity (MVPA) and vigorous physical activity (VPA). Mental health was measured using the Cantril Leader of Life Satisfaction, the WHO-5 index, Mental Health Inventory (MHI-5) and the Health Behaviour in School-Aged Children (HBSC) Symptom Checklist (HBSC-SCL). Data were analysed using bivariate (Pearson Correlation, t-test, one-way ANOVA) and multivariate (two-way ANOVA, ordinary least squares (OLS) regressions) analyses. In total, 8636 adolescents were included in this analysis. Higher participation in physical activity was associated with higher scores on the positive mental health indicators and lower scores on the mental health problems indicators. When modelled together, VPA was a stronger predictor of mental health than MVPA, especially in girls. For example, standardised beta coefficients for predicting MHI-5 were −0.09 for MVPA (p < 0.001) and −0.13 for VPA (p < 0.001) To our knowledge, this is the first study that looks at levels of physical activity as well as both positive mental health and mental health problems. The study highlights the need to encourage and enable adolescents, and especially girls, to participate in vigorous exercising as way of promoting positive mental health.