Background: Recurrent upper airway obstruction during sleep is a common feature of obstructive sleep apnea (OSA). Risk factors for the development of OSA include obesity, male gender and smoking. In addition, anatomical factors contribute to the development of the disease; however, the heritability of the anatomical structures that determine upper airway narrowing is poorly understood. In this study, we aimed to investigate the background of anatomical structures associated with upper airway narrowing in discordant monozygotic (MZ) twin pairs. Methods: 33 adult MZ twin pairs (median age and Q1-Q3: 50 (42–56) years) from the Hungarian Twin Registry underwent head and neck MR (Philips Ingenia 1.5 T). T1- and T2-weighted images in sagittal, coronal and axial planes were used to measure cephalometric, soft tissue and adipose tissue structures. In addition, the twin pairs underwent carotid and femoral ultrasound scans (Samsung RS85) and full-body composition measurements (OMRON BF500). The analysis of discordant MZ twins for anatomical markers in relation to clinical background, blood test, vascular ultrasound and body composition results was performed using a paired permutation test. Results: We found a significant association between parapharyngeal adipose tissue area and body weight, waist circumference and metabolism (p < 0.05). Submental adipose tissue thickness showed an association with lower body muscle percentage (<0.05). Carotid intima-media thickness showed a negative association with parapharyngeal adipose tissue, tongue volume and submental adipose tissue thickness (<0.05). Conclusions: Our study found a significant association between anatomical structures potentially involved in upper airway narrowing and obesity-related markers such as weight, BMI, hip and waist circumference, and whole body composition analysis results (body fat percentage, visceral fat percentage, muscle percentage). This study may help to better understand the background of anatomical structures potentially involved in upper airway narrowing and the possible development of obstructive sleep apnea.