Depression and anxiety are mental health conditions that can significantly impact individuals’ well-being, with various risk factors contributing to their severity. This study aimed to characterise the prevalence of anxiety and depression among a university population and examine the associated sociodemographic factors. Methods: A descriptive cross-sectional study was conducted with 394 students from a higher education institution. Sociodemographic factors were analysed using two validated instruments: the Hamilton Anxiety Scale and the PHQ-9 (Depression Symptom Test). The statistical analyses included Pearson’s chi-square test and Fisher’s exact test to assess associations. Results: The mental health outcomes were significantly influenced by several factors. Key variables associated with anxiety and depression included academic overload (* p < 0.001), gender (* p < 0.001), father’s education level (* p < 0.001), socioeconomic status (* p < 0.001), and sexual orientation (* p < 0.001). These findings highlight the complex interplay between sociodemographic factors and mental health in university students. Conclusions: Early identification and interventions for anxiety and depression should be considered to provide timely and relevant mental health programmes for university students.