University students are at increased risk of developing burnout and psychological distress from high academic workloads and performance expectations. The purpose of this study is to analyze the relationship between psychological and lifestyle variables and academic burnout, as well as to identify burnout risk profiles in psychology students. This study used a cross-sectional design and included 274 Portuguese psychology students, the majority being undergraduates (72.6%). Participants were assessed on psychological well-being, psychological distress, difficulties in emotional regulation, type of diet, physical activity, sleep quality, and burnout. The results showed that psychological distress, difficulties in emotional regulation, and sleep quality were positively associated with burnout, while psychological well-being was negatively associated. Using machine learning algorithms, two distinct profiles were found: “Burnout Risk” and “No Risk”. A total of 62 participants were identified as belonging to the burnout risk profile, showing higher levels of distress, emotional regulation difficulties, poor psychological well-being and sleep quality, pro-inflammatory diet, and less physical activity. The accuracy of the three machine learning models—Random Forest, XGBoost, and Support Vector Machine—was 95.06%, 93.82%, and 97.53%, respectively. These results suggest the importance of health promotion within university settings, together with mental health strategies focused on adaptive psychological functioning, to prevent the risk of burnout.