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(1) Background: The identification of patients at risk for hepatitis B and C viral infection is a challenge for the clinicians and public health specialists. The aim of this study was to evaluate and compare the predictive performances of four machine learning-based models for the prediction of HBV and HCV status. (2) Methods: This prospective cohort screening study evaluated adults from the North-Eastern and South-Eastern regions of Romania between January 2022 and November 2022 who underwent viral hepatitis screening in their family physician’s offices. The patients’ clinical characteristics were extracted from a structured survey and were included in four machine learning-based models: support vector machine (SVM), random forest (RF), naïve Bayes (NB), and K nearest neighbors (KNN), and their predictive performance was assessed. (3) Results: All evaluated models performed better when used to predict HCV status. The highest predictive performance was achieved by KNN algorithm (accuracy: 98.1%), followed by SVM and RF with equal accuracies (97.6%) and NB (95.7%). The predictive performance of these models was modest for HBV status, with accuracies ranging from 78.2% to 97.6%. (4) Conclusions: The machine learning-based models could be useful tools for HCV infection prediction and for the risk stratification process of adult patients who undergo a viral hepatitis screening program.