Background: Although the internet facilitates access to a wide range of knowledge and evidence, overuse among young people is associated with lower wellbeing and psychosomatic symptoms. The aim of this cross-sectional study is to explore the relationship between internet use, mental wellbeing, and psychosomatic symptoms among university students in Slovenia. Methods: We used correlation matrix plots to identify correlated symptoms and multivariate logistic regression to analyze the relationship between the time spent on the internet or computer and psychosomatic symptoms controlling for gender. Symptoms were measured using the Health Behavior of School Children scale. Results: Out of 464 students, the majority (64.7%, n = 300) were healthcare students and 35.3% (n = 164) were computer science students. Among somatic symptoms, headaches were associated with more time spent on the computer (r = −0.17, p < 0.001) and were significantly more prevalent in computer science students compared to health science students (χ2(1) = 8.52, p = 0.004). Time spent using the internet for spare time activities was associated with lower nervousness (r = 0.15, p = 0.005). Conclusions: Computer science students reported more frequent psychological symptoms compared to health science students and less somatic symptoms.