Background/Objectives: Aortic stenosis (AS) is the most prevalent valvular disease among older adults. Although obstructive sleep apnea (OSA) has been linked to adverse cardiovascular outcomes, its specific impact on patients with severe AS remains unclear. This study aimed to determine the prevalence of OSA and its influence on postoperative recovery following aortic valve replacement. Methods: A prospective case-control study was conducted at the Instituto Nacional de Cardiología Ignacio Chávez. Patients aged 40–80 years with echocardiographically confirmed severe AS were categorized into groups with and without OSA, based on respiratory polygraphy (Apnea–Hypopnea Index [AHI] threshold of >15 events per hour). Clinical, biochemical, echocardiographic, body composition, and hemodynamic parameters were assessed. Daytime sleepiness and sleep quality were evaluated using validated questionnaires. Inflammatory biomarkers were also analyzed. This study was approved by the institutional ethics committee. Results: Of the 30 patients included, 66.6% were diagnosed with OSA. Compared to non-OSA patients, those with OSA had a higher left ventricular mass index (160 vs. 108; p = 0.001), greater postoperative increases in central venous pressure [8 (8–10) vs. 8 (6–8); p = 0.037], and lower mixed venous oxygen saturation within the first 24 h (69.2 vs. 76; p = 0.027). OSA patients also had longer hospital stays (11 vs. 8 days; p = 0.014). Trends toward a heightened subclinical inflammatory state were noted in the OSA group. Conclusions: OSA is frequent and underdiagnosed in patients with severe AS and is associated with more complicated postoperative recovery. Systematic OSA screening is recommended for candidates undergoing aortic valve surgery.