This study aimed to analyze the associations of obstructive sleep apnea (OSA) with dental parameters while controlling for socio-demographics, health-related habits, and each of the diseases comprising metabolic syndrome (MetS), its consequences, and related conditions. We analyzed data from the dental, oral, and medical epidemiological (DOME) cross-sectional records-based study that combines comprehensive socio-demographic, medical, and dental databases of a nationally representative sample of military personnel for one year. Analysis included statistical and machine learning models. The study included 132,529 subjects; of these, 318 (0.2%) were diagnosed with OSA. The following parameters maintained a statistically significant positive association with OSA in the multivariate binary logistic regression analysis (descending order from highest to lowest OR): obesity (OR = 3.104 (2.178–4.422)), male sex (OR = 2.41 (1.25–4.63)), periodontal disease (OR = 2.01 (1.38–2.91)), smoking (OR = 1.45 (1.05–1.99)), and age (OR = 1.143 (1.119–1.168)). Features importance generated by the XGBoost machine learning algorithm were age, obesity, and male sex (located on places 1–3), which are well-known risk factors of OSA, as well as periodontal disease (fourth place) and delivered dental fillings (fifth place). The Area Under Curve (AUC) of the model was 0.868 and the accuracy was 0.92. Altogether, the findings supported the main hypothesis of the study, which was that OSA is linked to dental morbidity, in particular to periodontitis. The findings highlight the need for dental evaluation as part of the workup of OSA patients and emphasizes the need for dental and general medical authorities to collaborate by exchanging knowledge about dental and systemic morbidities and their associations. The study also highlights the necessity for a comprehensive holistic risk management strategy that takes systemic and dental diseases into account.