Regular physical activity (PA) and, more specifically, exercise, is associated with lower levels of stress, depression, and anxiety. The aim of this repeated cross-sectional pilot study was to investigate the impact of participating in PA on the mental health of young adults in Greece during the COVID-19 pandemic. The study was carried out during two quarantine periods: Survey I on 5 May 2020, and Survey II on 30 April 2021. The Hamilton Anxiety (HAM-A) and Beck Depression Inventory-II (BDI-II) scales and the level of PA were used to assess a sample of individuals aged between 18 and 26 years old. In 2020 and 2021, a total of 268 (33.9% males) and 380 (37.1% females) subjects participated in the studies, respectively. According to the findings, the vast majority of the participants in both samples reported that they are physically active (p = 0.86), while they consider exercise as a significant health factor (p = 0.10). Moreover, anxiety levels statistically significant increased (p = 0.001), while depression levels remained relatively stable with a slight increase of approximately (p > 0.05). Additionally, in both surveys, individuals who engaged in a PA program exhibited reduced levels of depression and anxiety (p = 0.001). Also, gender appears to influence anxiety and depression levels, while a lack of exercise exacerbates these measures in both genders when compared to physically active individuals. Concludingly, it is crucial for public health strategies to include interventions that promote safe PA in the event of future lockdowns or similar emergencies.