Obstructive sleep apnea (OSA) is a global health concern and is typically diagnosed using in-laboratory polysomnography (PSG). However, PSG is highly time-consuming and labor-intensive. We, therefore, developed machine learning models based on easily accessed anthropometric features to screen for the risk of moderate to severe and severe OSA. We enrolled 3503 patients from Taiwan and determined their PSG parameters and anthropometric features. Subsequently, we compared the mean values among patients with different OSA severity and considered correlations among all participants. We developed models based on the following machine learning approaches: logistic regression, k-nearest neighbors, naïve Bayes, random forest (RF), support vector machine, and XGBoost. Collected data were first independently split into two data sets (training and validation: 80%; testing: 20%). Thereafter, we adopted the model with the highest accuracy in the training and validation stage to predict the testing set. We explored the importance of each feature in the OSA risk screening by calculating the Shapley values of each input variable. The RF model achieved the highest accuracy for moderate to severe (84.74%) and severe (72.61%) OSA. The level of visceral fat was found to be a predominant feature in the risk screening models of OSA with the aforementioned levels of severity. Our machine learning models can be employed to screen for OSA risk in the populations in Taiwan and in those with similar craniofacial structures.