Background: COVID-19 containment measures and the uncertainties associated with the pandemic may have contributed to changes in mental health risks and mental health problems in university students. Due to the high burden of the disease, depression is of particular concern. However, knowledge about the prevalence of depressive symptoms in Swiss university students during the pandemic is limited. We therefore assessed the prevalence of depressive symptoms and their change during the COVID-19 pandemic in a large sample of Swiss university students. Methods: We assessed depressive symptoms in two cross-sectional cohorts of university students (n = 3571) in spring and autumn 2020 during the COVID-19 pandemic and compared them with a matched sample of the Swiss national population (n = 2328). Binary logistic regression models estimated prevalence with corresponding 95% confidence intervals (95% CI). Results: Adjusted prevalence of depressive symptoms in female (30.8% (95% CI: 28.6–33.0)) and male students (24.8% (95% CI: 21.7–28.1)) was substantially higher than in the matching female (10.9% (95% CI: 8.9–13.2)) and male (8.5% (6.6–11.0)) pre-pandemic national population. Depressive symptoms in the two consecutive student cohorts did not significantly differ. Conclusions: More than a quarter of Swiss university students reported depressive symptoms during the COVID-19 pandemic, which was substantially higher as compared to the matched general population. Universities should introduce measures to support students in such times of crisis and gain an understanding of the factors impacting mental health positively or negatively and related to university structures and procedures.