Background: This study aims to assess how well several machine learning (ML) algorithms predict the physical, social, and mental health condition of university students. Objectives: The physical health measurements used in the study include BMI (Body Mass Index), %BF (percentage of Body Fat), BSC (Blood Serum Cholesterol), SBP (Systolic Blood Pressure), and DBP (Diastolic Blood Pressure). Methods: The mental health evaluation relied on the following methods: PHQ-9 (Patient Health Questionnaire-9), ISI (Insomnia Severity Index), GAD-7 (Generalized Anxiety Disorder Scale), and SBQ-R (Suicidal Behaviors Questionnaire-Revised). The study assessed KEYES, the comprehensive social health indicator. The study uses a famous methodology for training and testing four well-known ML algorithms, namely the K-nearest neighbors algorithm, decision trees, Naïve Bayes, and the random forest algorithm. Results and Conclusions: The recall value of the RF algorithm is higher by 2.0%, 4.15%, and 11.25%, respectively. The F-score value of the RF algorithm is also the highest. The differences amount to 4.56% ("Naïve Bayes"), 2.50% ("DT"), and 11.20% ("K-NN"). Accuracy, Precision, Recall, and F-score were used to assess the researched ML algorithms' prediction ability. With a 99.40% prediction accuracy, a 97.60% precision, a 99.30% recall, and an F-score value of 98.70%, the Random Forest method performed the best. ML algorithms can serve as tools for the prediction of physical, mental, and social health state of patients, including students, but they have a rather narrow scope of application and do not cover all aspects of health.