(1) Background: Prenatal care providers face a continuous challenge in screening for intrauterine growth restriction (IUGR) and preeclampsia (PE). In this study, we aimed to assess and compare the predictive accuracy of four machine learning algorithms in predicting the occurrence of PE, IUGR, and their associations in a group of singleton pregnancies; (2) Methods: This observational prospective study included 210 singleton pregnancies that underwent first trimester screenings at our institution. We computed the predictive performance of four machine learning-based methods, namely decision tree (DT), naïve Bayes (NB), support vector machine (SVM), and random forest (RF), by incorporating clinical and paraclinical data; (3) Results: The RF algorithm showed superior performance for the prediction of PE (accuracy: 96.3%), IUGR (accuracy: 95.9%), and its subtypes (early onset IUGR, accuracy: 96.2%, and late-onset IUGR, accuracy: 95.2%), as well as their association (accuracy: 95.1%). Both SVM and NB similarly predicted IUGR (accuracy: 95.3%), while SVM outperformed NB (accuracy: 95.8 vs. 94.7%) in predicting PE; (4) Conclusions: The integration of machine learning-based algorithms in the first-trimester screening of PE and IUGR could improve the overall detection rate of these disorders, but this hypothesis should be confirmed in larger cohorts of pregnant patients from various geographical areas.