Introduction Depression and anxiety are two types of mental disorders. Individuals with depression usually experience depressed mood, loss of interest or enjoyment, and reduced energy, leading to increased fatigability that diminishes their activity. Meanwhile, anxiety disorders refer to a group of mental disorders characterized by feelings of anxiety and fear. The coronavirus disease 2019 (COVID-19) pandemic has led to mass quarantine, isolation, and lockdowns worldwide, which have impacted the population's mental health. In Saudi Arabia, a study showed that 17.1% and 10.5% of the population had moderate-to-severe features of depression and anxiety, respectively. Demonstrating the prevalence of depression and anxiety in educational institutions is essential. This study aimed to measure the prevalence of depression and anxiety among students at Qassim University during the COVID-19 pandemic. Methods This cross-sectional study was conducted at Qassim University, Saudi Arabia. The students were selected using a multistage random sampling technique. An online questionnaire was sent to the selected students via e-mail and social media platforms. The questionnaire contained three parts: the first part included socio-demographic questions, the second part contained the Patient Health Questionnaire-9 (PHQ-9) to measure depression, and the third part contained the Generalized Anxiety Disorder-7 (GAD-7) questionnaire to measure anxiety. Results In total, 411 university students completed the questionnaire (response rate = 75%). The prevalence of depression and anxiety was 40.6% and 29.4%, respectively. Females had higher levels of depression and anxiety than men (p < 0.001). The College of Arabic Language and Social Studies (CALSS) had the highest prevalence of depression and anxiety (42.9% and 30.6%, respectively). Conclusion We found a high post-pandemic prevalence of depression and anxiety among the students at Qassim University. Our findings demonstrate the need for psychological intervention programs for the students of Qassim University.